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1.
We introduce a spanning set of Beilinson–Lusztig–MacPherson type, {A(j, r)}
A,j
, for affine quantum Schur algebras
S\vartriangle(n, r){{{\boldsymbol{\mathcal S}}_\vartriangle}(n, r)} and construct a linearly independent set {A(j)}
A,j
for an associated algebra
[^(K)]\vartriangle(n){{{\boldsymbol{\widehat{\mathcal K}}}_\vartriangle}(n)} . We then establish explicitly some multiplication formulas of simple generators
E\vartriangleh,h+1(0){E^\vartriangle_{h,h+1}}(\mathbf{0}) by an arbitrary element A(j) in
[^(K)]\vartriangle(n){{\boldsymbol{\widehat{{{\mathcal K}}}}_\vartriangle(n)}} via the corresponding formulas in
S\vartriangle(n, r){{{\boldsymbol{\mathcal S}}_\vartriangle(n, r)}} , and compare these formulas with the multiplication formulas between a simple module and an arbitrary module in the Ringel–Hall
algebras
\mathfrak H\vartriangle(n){{{\boldsymbol{\mathfrak H}_\vartriangle(n)}}} associated with cyclic quivers. This allows us to use the triangular relation between monomial and PBW type bases for
\mathfrak H\vartriangle(n){{\boldsymbol{\mathfrak H}}_\vartriangle}(n) established in Deng and Du (Adv Math 191:276–304, 2005) to derive similar triangular relations for
S\vartriangle(n, r){{{\boldsymbol{\mathcal S}}_\vartriangle}(n, r)} and
[^(K)]\vartriangle(n){{\boldsymbol{\widehat{\mathcal K}}}_\vartriangle}(n) . Using these relations, we then show that the subspace
\mathfrak A\vartriangle(n){{{\boldsymbol{\mathfrak A}}_\vartriangle}(n)} of
[^(K)]\vartriangle(n){{\boldsymbol{\widehat{{{\mathcal K}}}}_\vartriangle}(n)} spanned by {A(j)}
A,j
contains the quantum enveloping algebra
U\vartriangle(n){{{\mathbf U}_\vartriangle}(n)} of affine type A as a subalgebra. As an application, we prove that, when this construction is applied to quantum Schur algebras S(n,r){\boldsymbol{\mathcal S}(n,r)} , the resulting subspace
\mathfrak A\vartriangle(n){{{{\boldsymbol{\mathfrak A}}_\vartriangle}(n)}} is in fact a subalgebra which is isomorphic to the quantum enveloping algebra of
\mathfrakgln{\mathfrak{gl}_n} . We conjecture that
\mathfrak A\vartriangle(n){{{{{\boldsymbol{\mathfrak A}}_\vartriangle}(n)}}} is a subalgebra of
[^(K)]\vartriangle(n){{\boldsymbol{\widehat{{{\mathcal K}}}}_\vartriangle}(n)} . 相似文献
2.
Gerald W. Schwarz 《Journal of Fixed Point Theory and Applications》2011,10(2):359-367
Let K be a compact Lie group and W a finite-dimensional real K-module. Let X be a K-stable real algebraic subset of W. Let I(X){\mathcal{I}(X)} denote the ideal of X in
\mathbbR[W]{\mathbb{R}[W]} and let IK(X){\mathcal{I}_{K}(X)} be the ideal generated by I(X)K{\mathcal{I}(X)^{K}} . We find necessary conditions and sufficient conditions for I(X) = IK(X){{\mathcal{I}(X) = \mathcal{I}_{K}(X)}} and for ?{IK(X)} = I(X){{\sqrt{\mathcal{I}_{K}(X)} = \mathcal{I}(X)}} . We consider analogous questions for actions of complex reductive groups. 相似文献
3.
By a totally regular parallelism of the real projective 3-space
P3:=PG(3, \mathbb R){\Pi_3:={{\rm PG}}(3, \mathbb {R})} we mean a family T of regular spreads such that each line of Π
3 is contained in exactly one spread of T. For the investigation of totally regular parallelisms the authors mainly employ Klein’s correspondence λ of line geometry and the polarity π
5 associated with the Klein quadric H
5 (for details see Chaps. 1 and 3). The λ-image of a totally regular parallelism T is a hyperflock of H
5, i.e., a family H of elliptic subquadrics of H
5 such that each point of H
5 is on exactly one subquadric of H. Moreover, {p5(span l(X))|X ? T}=:HT{\{\pi_5({{\rm span}} \,\lambda(\mathcal {X}))\vert\mathcal {X}\in\bf{T}\}=:\mathcal {H}_{\bf{T}}} is a hyperflock determining line set, i.e., a set Z{\mathcal {Z}} of 0-secants of H
5 such that each tangential hyperplane of H
5 contains exactly one line of Z{\mathcal {Z}} . We say that dim(span HT)=:dT{{{\rm dim}}({{\rm span}}\,\mathcal {H}_{\bf{T}})=:d_{\bf{T}}} is the dimension of
T and that T is a d
T
- parallelism. Clifford parallelisms and 2-parallelisms coincide. The examples of non-Clifford parallelisms exhibited in Betten
and Riesinger [Result Math 47:226–241, 2004; Adv Geom 8:11–32, 2008; J Geom (to appear)] are totally regular and of dimension
3. If G{\mathcal{G}} is a hyperflock determining line set, then {l-1 (p5(X) ?H5) | X ? G}{\{\lambda^{-1}\,{\rm (}\pi_5(X){\,\cap H_5)\,|\, X\in\mathcal{G}\}}} is a totally regular parallelism. In the present paper the authors construct examples of topological (see Definition 1.1)
4- and 5-parallelisms via hyperflock determining line sets. 相似文献
4.
Aziz El Kacimi Alaoui 《Mathematische Annalen》2010,347(4):885-897
In (Ann Sc ENS Sér 3 4:361–380, 1887) Guichard proved that, for any holomorphic function g on ${{\mathbb C}}In (Ann Sc ENS Sér 3 4:361–380, 1887) Guichard proved that, for any holomorphic function g on
\mathbb C{{\mathbb C}}, there exists a holomorphic function h (on
\mathbb C{{\mathbb C}}) such that h - h °t = g{h - h \circ \tau = g} where τ is the translation by 1 on
\mathbb C{{\mathbb C}}. In this note we prove an analogous of this theorem in a more general situation. Precisely, let (M,F){(M,{\mathcal F})} be a complex simple foliation whose leaves are simply connected non compact Riemann surfaces and γ an automorphism of F{{\mathcal F}} which fixes each leaf and acts on it freely and properly. Then, the vector space HF(M){{\mathcal H}_{\mathcal F}(M)} of leafwise holomorphic functions is not reduced to functions constant on the leaves and for any g ? HF(M){g \in {\mathcal H}_{\mathcal F}(M)}, there exists h ? HF(M){h \in {\mathcal H}_{\mathcal F}(M)} such that h - h °g = g{h - h \circ \gamma = g}. From the proof of this theorem we derive a foliated version of Mittag–Leffler Theorem. 相似文献
5.
Bernhard Burgstaller 《Monatshefte für Mathematik》2009,265(4):1-11
There exists a separable exact C*-algebra A which contains all separable exact C*-algebras as subalgebras, and for each norm-dense measure μ on A and independent μ-distributed random elements x
1, x
2, ... we have
limn ? ¥\mathbb P(C*(x1,?,xn) is nuclear)=0{\rm {lim}}_{n \rightarrow \infty}\mathbb {P}(C^*(x_1,\ldots,x_n) \mbox{ is nuclear})=0. Further, there exists a norm-dense non-atomic probability measure μ on the Cuntz algebra O2{\mathcal {O}_2} such that for an independent sequence x
1, x
2, ... of μ-distributed random elements x
i
we have
lim infn ? ¥\mathbb P(C*(x1,?,xn) is nuclear)=0{\rm {lim\, inf}}_{n \rightarrow \infty}\mathbb {P}(C^*(x_1,\ldots,x_n) \mbox{ is nuclear})=0. We introduce the notion of the stochastic rank for a unital C*-algebra and prove that the stochastic rank of C([0, 1]
d
) is d. 相似文献
6.
We consider the class of minimal surfaces given by the graphical strips ${{\mathcal S}}We consider the class of minimal surfaces given by the graphical strips S{{\mathcal S}} in the Heisenberg group
\mathbb H1{{\mathbb {H}}^1} and we prove that for points p along the center of
\mathbb H1{{\mathbb {H}}^1} the quantity
\fracsH(S?B(p,r))rQ-1{\frac{\sigma_H(\mathcal S\cap B(p,r))}{r^{Q-1}}} is monotone increasing. Here, Q is the homogeneous dimension of
\mathbb H1{{\mathbb {H}}^1} . We also prove that these minimal surfaces have maximum volume growth at infinity. 相似文献
7.
Kyriakos Keremedis 《Mathematical Logic Quarterly》2012,58(3):130-138
Given a set X, $\mathsf {AC}^{\mathrm{fin}(X)}$ denotes the statement: “$[X]^{<\omega }\backslash \lbrace \varnothing \rbrace$ has a choice set” and $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )$ denotes the family of all closed subsets of the topological space $\mathbf {2}^{X}$ whose definition depends on a finite subset of X. We study the interrelations between the statements $\mathsf {AC}^{\mathrm{fin}(X)},$ $\mathsf {AC}^{\mathrm{fin}([X]^{<\omega })},$ $\mathsf {AC}^{\mathrm{fin} (F_{n}(X,2))},$ $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$ and “$\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$has a choice set”. We show:
- (i) $\mathsf {AC}^{\mathrm{fin}(X)}$ iff $\mathsf {AC}^{\mathrm{fin}([X]^{<\omega } )}$ iff $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set iff $\mathsf {AC}^{\mathrm{fin}(F_{n}(X,2))}$.
- (ii) $\mathsf {AC}_{\mathrm{fin}}$ ($\mathsf {AC}$ restricted to families of finite sets) iff for every set X, $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set.
- (iii) $\mathsf {AC}_{\mathrm{fin}}$ does not imply “$\mathcal {K}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set($\mathcal {K}(\mathbf {X})$ is the family of all closed subsets of the space $\mathbf {X}$)
- (iv) $\mathcal {K}(\mathbf {2}^{X})\backslash \lbrace \varnothing \rbrace$ implies $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$ but $\mathsf {AC}^{\mathrm{fin}(X)}$ does not imply $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$.
8.
Andrea Vietri 《Order》2005,22(3):201-221
A class of ranked posets {(D
h
k
, ≪)} has been recently defined in order to analyse, from a combinatorial viewpoint, particular systems of real homogeneous
inequalities between monomials. In the present paper we focus on the posets D
2
k
, which are related to systems of the form {x
a
x
b
*
abcd
x
c
x
d
: 0 ≤ a, b, c, d ≤ k, *
abcd
∈ {<, >}, 0 < x
0 < x
1 < ...< x
k}. As a consequence of the general theory, the logical dependency among inequalities is adequately captured by the so-defined
posets . These structures, whose elements are all the D
2
k
's incomparable pairs, are thoroughly surveyed in the following pages. In particular, their order ideals – crucially significant
in connection with logical consequence – are characterised in a rather simple way. In the second part of the paper, a class
of antichains is shown to enjoy some arithmetical properties which make it an efficient tool for detecting incompatible systems, as well
as for posing some compatibility questions in a purely combinatorial fashion. 相似文献
9.
Bernhard Burgstaller 《Monatshefte für Mathematik》2009,157(1):1-11
There exists a separable exact C*-algebra A which contains all separable exact C*-algebras as subalgebras, and for each norm-dense measure μ on A and independent μ-distributed random elements x
1, x
2, ... we have . Further, there exists a norm-dense non-atomic probability measure μ on the Cuntz algebra such that for an independent sequence x
1, x
2, ... of μ-distributed random elements x
i
we have . We introduce the notion of the stochastic rank for a unital C*-algebra and prove that the stochastic rank of C([0, 1]
d
) is d.
B. Burgstaller was supported by the Austrian Schr?dinger stipend J2471-N12. 相似文献
10.
Chen Yonglin 《应用数学学报(英文版)》2001,17(1):114-120
This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse AT,S(2)A_{T,S}^{(2)} and give some of their applications. 相似文献
11.
Let R be a noetherian ring,
\mathfraka{\mathfrak{a}} an ideal of R, and M an R-module. We prove that for a finite module M, if
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is minimax for all i ≥ r ≥ 1, then
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is artinian for i ≥ r. A local–global principle for minimax local cohomology modules is shown. If
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is coatomic for i ≤ r (M finite) then
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is finite for i ≤ r. We give conditions for a module which is locally minimax to be a minimax module. A non-vanishing theorem and some vanishing
theorems are proved for local cohomology modules. 相似文献
12.
Go Hirasawa 《Integral Equations and Operator Theory》2011,70(3):363-378
We introduce a metric in the set S(H){{\mathcal S}(H)} of all semiclosed operators in a Hilbert space H, and its topological structures are studied. 相似文献
13.
Invariant notions of a class of Segre varieties S(m)(2){\mathcal{S}_{(m)}(2)} of PG(2
m
− 1, 2) that are direct products of m copies of PG(1, 2), m being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that
contains S(m)(2){\mathcal{S}_{(m)}(2)} and is invariant under its projective stabiliser group GS(m)(2){G_{{\mathcal{S}}_{(m)}(2)}} . By embedding PG(2
m
− 1, 2) into PG(2
m
− 1, 4), a basis of the latter space is constructed that is invariant under GS(m)(2){G_{{\mathcal{S}}_{(m)}(2)}} as well. Such a basis can be split into two subsets whose spans are either real or complex-conjugate subspaces according
as m is even or odd. In the latter case, these spans can, in addition, be viewed as indicator sets of a GS(m)(2){G_{{\mathcal{S}}_{(m)}(2)}} -invariant geometric spread of lines of PG(2
m
− 1, 2). This spread is also related with a GS(m)(2){G_{{\mathcal{S}}_{(m)}(2)}} -invariant non-singular Hermitian variety. The case m = 3 is examined in detail to illustrate the theory. Here, the lines of the invariant spread are found to fall into four distinct
orbits under GS(m)(2){G_{{\mathcal{S}}_{(m)}(2)}} , while the points of PG(7, 2) form five orbits. 相似文献
14.
Let M be an n-generator projective MV-algebra. Then there is a rational polyhedron P in the n-cube [0, 1]
n
such that M is isomorphic to the MV-algebra M(P){{\rm{\mathcal {M}}}(P)} of restrictions to P of the McNaughton functions of the free n-generator MV-algebra. P necessarily contains a vertex vP of the n-cube. We characterize those polyhedra contained in the n-cube such that M(P){{\mathcal {M}}(P)} is projective. In particular, if the rational polyhedron P is a union of segments originating at some fixed vertex vP of the n-cube, then M(P){{\mathcal {M}}(P)} is projective. Using this result, we prove that if A = M(P){A = {\mathcal {M}}(P)} and B = M(Q){B = {\mathcal {M}}(Q)} are projective, then so is the subalgebra of A × B given by {(f, g) | f(v
P
) = g(v
Q
), and so is the free product
A \coprod B{A \coprod B} . 相似文献
15.
A. V. Kotikov L. N. Lipatov A. I. Onishchenko V. N. Velizhanin 《Theoretical and Mathematical Physics》2007,150(2):213-224
We present results for the universal anomalous dimension γun(j) of Wilson twist-2 operators in the
supersymmetric Yang-Mills theory in the first three orders of the perturbation theory. We obtain these expressions by extracting
the most complicated terms from the corresponding anomalous dimensions in QCD. The result obtained agrees with the hypothesis
of the integrability of the
supersymmetric Yang-Mills theory in the context of the AdS/CFT correspondence.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 249–262, February, 2007. 相似文献
16.
Let H be a Hilbert space and A, B: H ⇉ H two maximal monotone operators. In this paper, we investigate the properties of the following proximal type algorithm:
where (λ
n
) is a sequence of positive steps. Algorithm may be viewed as the discretized equation of a nonlinear oscillator subject to friction. We prove that, if 0 ∈ int (A(0)) (condition of dry friction), then the sequence (x
n
) generated by is strongly convergent and its limit x
∞ satisfies 0 ∈ A(0) + B(x
∞). We show that, under a general condition, the limit x
∞ is achieved in a finite number of iterations. When this condition is not satisfied, we prove in a rather large setting that
the convergence rate is at least geometrical. 相似文献
17.
Consider oriented surfaces immersed in
. Associated to them,
here are studied pairs of transversal foliations with
singularities, defined on the Elliptic region, where the
Gaussian curvature
, given
by the product of the principal curvatures
k
1,
k
2 is
positive. The leaves of the foliations are the
lines of harmonic mean
curvature, also called characteristic or
diagonal lines, along which
the normal curvature of the immersion is given by
, where
is the
arithmetic mean curvature. That is,
is the harmonic mean of the
principal curvatures k
1,
k
2 of
the immersion. The singularities of the foliations are the
umbilic points and
parabolic curves, where
k
1 =
k
2 and
, respectively.Here are determined the structurally stable patterns of
harmonic mean curvature lines
near the umbilic points, parabolic
curves and harmonic mean
curvature cycles, the periodic leaves of the
foliations. The genericity of these patterns is
established.This provides the three essential local ingredients to
establish sufficient conditions, likely to be also necessary,
for Harmonic Mean Curvature Structural
Stability of immersed surfaces. This study, outlined
towards the end of the paper, is a natural analog and complement
for that carried out previously by the authors for the
Arithmetic Mean Curvature and
the Asymptotic Structural
Stability of immersed surfaces, [13, 14, 17], and
also extended recently to the case of the
Geometric Mean Curvature
Configuration [15].The first author was partially supported by FUNAPE/UFG.
Both authors are fellows of CNPq.
This work was done under the project PRONEX/FINEP/MCT -
Conv. 76.97.1080.00 - Teoria Qualitativa das Equações Diferenciais
Ordinárias and CNPq - Grant 476886/2001-5. 相似文献
18.
Let ${\mathcal {H}_{1}}Let H1{\mathcal {H}_{1}} and H2{\mathcal {H}_{2}} be separable Hilbert spaces, and let A ? B(H1), B ? B(H2){A \in \mathcal {B}(\mathcal {H}_{1}),\, B \in \mathcal {B}(\mathcal {H}_{2})} and C ? B(H2, H1){C \in \mathcal {B}(\mathcal {H}_{2},\, \mathcal {H}_{1})} be given operators. A necessary and sufficient condition is given for ${\left(\begin{smallmatrix}A &\enspace C\\ X &\enspace B \end{smallmatrix}\right)}${\left(\begin{smallmatrix}A &\enspace C\\ X &\enspace B \end{smallmatrix}\right)} to be a right (left) invertible operator for some X ? B(H1, H2){X \in \mathcal {B}(\mathcal {H}_{1},\, \mathcal {H}_{2})}. Furthermore, some related results are obtained. 相似文献
19.
In this second paper, we study the case of substitution tilings of
\mathbb Rd{{\mathbb R}^d} . The substitution on tiles induces substitutions on the faces of the tiles of all dimensions j = 0, . . . , d − 1. We reconstruct the tiling’s equivalence relation in a purely combinatorial way using the AF-relations given by the lower
dimensional substitutions. We define a Bratteli multi-diagram B{{\mathcal B}} which is made of the Bratteli diagrams Bj, j=0, ?d{{\mathcal B}^j, j=0, \ldots d} , of all those substitutions. The set of infinite paths in Bd{{\mathcal B}^d} is identified with the canonical transversal Ξ of the tiling. Any such path has a “border”, which is a set of tails in Bj{{\mathcal B}^j} for some j ≤ d, and this corresponds to a natural notion of border for its associated tiling. We define an étale equivalence relation RB{{\mathcal R}_{\mathcal B}} on B{{\mathcal B}} by saying that two infinite paths are equivalent if they have borders which are tail equivalent in Bj{{\mathcal B}^j} for some j ≤ d. We show that RB{{\mathcal R}_{\mathcal B}} is homeomorphic to the tiling’s equivalence relation RX{{\mathcal R}_\Xi} . 相似文献
20.
I. P. Il’inskaya 《Ukrainian Mathematical Journal》2009,61(7):1113-1122
We study the arithmetic of a semigroup MP\mathcal{M}_{\mathcal{P}} of functions with operation of multiplication representable in the form f(x) = ?n = 0¥ ancn(x) ( an 3 0,?n = 0¥ an = 1 ) f(x) = \sum\nolimits_{n = 0}^\infty {{a_n}{\chi_n}(x)\quad \left( {{a_n} \ge 0,\sum\nolimits_{n = 0}^\infty {{a_n} = 1} } \right)} , where { cn }n = 0¥ \left\{ {{\chi_n}} \right\}_{n = 0}^\infty is a system of multiplicative functions that are generalizations of the classical Walsh functions. For the semigroup MP\mathcal{M}_{\mathcal{P}}, analogs of the well-known Khinchin theorems related to the arithmetic of a semigroup of probability measures in R
n
are true. We describe the class I0(MP)I_0(\mathcal{M}_{\mathcal{P}}) of functions without indivisible or nondegenerate idempotent divisors and construct a class of indecomposable functions that
is dense in MP\mathcal{M}_{\mathcal{P}} in the topology of uniform convergence. 相似文献