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1.
In the examples of the N=2 super-Virasoro algebra and the affine
algebra, we investigate the construction of unitary representations of infinite-dimensional algebras in terms of collective excitations over a filled Dirac sea of fermionic or bosonic operators satisfying a generalized exclusion principle and represented by semi-infinite forms in the modes of one of the generators. We develop the methods for investigating properties of semi-infinite spaces (polynomial realization of the dual space) and for constructing the appropriate algebra action on these spaces (a filtration by subspaces similar to Demazure modules). We also consider relations of the semi-infinite realizations to the Rogers–Ramanujan-type identities, to the expression of coinvariants through meromorphic functions on products of Riemann surfaces with a prescribed behavior on multiple diagonals, and to some combinatorial facts; we also consider the relation between modular functors and fusion rules for the N=2 and
theories. 相似文献
2.
For
denote by
a polynomial of best weighted
-approximation to
on
of degree
. In the present paper, we are dealing with the asymptotic distribution of sign changes of the error functions
. 相似文献
3.
In this paper, we give a direct proof that every strongly
inverse semigroup can be embedded into a 0-semidirect product of a semilattice with zero by a group. As a corollary, we obtain a new proof of the structure theory of strongly
inverse semigroups described in [1]. We also prove that the strongly
inverse semigroups are precisely
inverse semigroups equipped with a
, idempotent pure prehomomorphism to a primitive inverse semigroup. 相似文献
4.
Crossed Modules and Quantum Groups in Braided Categories 总被引:2,自引:0,他引:2
Yu. N. Bespalov 《Applied Categorical Structures》1997,5(2):155-204
Let A be a Hopf algebra in a braided category
. Crossed modules over A are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category
of crossed modules is braided and is a concrete realization of a known general construction of a double or center of a monoidal category. For a quantum braided group
the corresponding braided category of modules
is identified with a full subcategory in
. The connection with cross products is discussed and a suitable cross product in the class of quantum braided groups is built. Majid–Radford theorem, which gives equivalent conditions for an ordinary Hopf algebra to be such a cross product, is generalized to the braided category. Majid's bosonization theorem is also generalized. 相似文献
5.
For semigroups (e
tA
)
t0 of operators on a Hilbert space, we give conditions guaranteeing trace estimates of the polynomial type
0$$
" align="middle" border="0">
, where
denotes the trace class. As an application we present higher order analogues of results due to E.B. Davies, B. Simon and M. van den Berg of the type
0$$
" align="middle" border="0">
, for certain unbounded domains
, e.g. spiny urchin domains. 相似文献
6.
Geoffery M.L. Powell 《K-Theory》1998,13(3):279-304
This paper defines and studies the polynomial filtration [pk
] of the shift functor
: F , where F is the category of functors between F-vector spaces over a finite field F. The functors [pk
] correspond to a system of functors (pk T):U U, related to Lannes'T-functor on the category U of unstable modules over the Steenrod algebra. The main results concern the behaviour of the quotients ~ s:=~/[ps-1~ filtrations by ~s-nilpotent functors are introduced and it is shown that the full subcategory of
s-nilpotent functors is thick. 相似文献
7.
Gerald Kuba 《Acta Mathematica Hungarica》2002,95(1-2):115-124
For a positive real parameter t, real numbers , , and
, we consider sums
, where
is the rounding error function, i.e.\
. Generalizing and improving the main result of Part I of the paper we show that there exists an absolute constant
such that
for all
, and all
. Further, we give applications concerning the circle problem with linear, polynomial, and general weight. 相似文献
8.
We propose new formulas for singular vectors in Verma modules over the affine Lie superalgebra
. We analyze the coexistence of singular vectors of different types and identify the twisted modules arising as submodules and quotient modules of
Verma modules. We show that with the twists (spectral flow transformations) properly taken into account, a resolution of irreducible representations can be constructed consisting of only the
modules. 相似文献
9.
Let
be a reductive Lie algebra over C. We say that a
-module M is a generalized Harish-Chandra module if, for some subalgebra
, M is locally
-finite and has finite
-multiplicities. We believe that the problem of classifying all irreducible generalized Harish-Chandra modules could be tractable. In this paper, we review the recent success with the case when
is a Cartan subalgebra. We also review the recent determination of which reductive in
subalgebras
are essential to a classification. Finally, we present in detail the emerging picture for the case when
is a principal 3-dimensional subalgebra. 相似文献
10.
11.
M. B. Zwyagina 《Journal of Mathematical Sciences》2002,112(4):4337-4347
Some applications of the general theorem on the existence of local duality for modules over Noetherian commutative rings are given. Let
be a Noetherian commutative ring, let
be a set of maximal ideals in
, and let
. Then the category of Artinian modules is dual to the category of Noetherian modules. Several structural results are proved, including the theorem on the structure of Artinian modules over principal ideal domains. For rings of special kinds, double centralizer theorems are proved. Bibliography: 5 titles. 相似文献
12.
13.
Andrew Ranicki 《K-Theory》1989,3(2):163-195
The cobordism groups of quadratic Poincaré complexes in an additive category with involution
are identified with the Wall L-groups of quadratic forms and formations in
, generalizing earlier work for modules over a ring with involution by avoiding kernels and cokernels. 相似文献
14.
Conditions for the oscillation of all solutions and for the existence of nonoscillatory solutions with polynomial growth at infinity are given for the system of differential-functional equations of neutral type
相似文献
15.
Let
be a polynomial with complex coefficients and define, for
,
where ||P|| is the euclidean norm of the polynomial P. By a theorem of Szegö
where
is the Mahler measure of F. Recently, J. Dégot proved an effective version of this result. In this paper we sharpen Dégot's result, under the additional hypotheses that F is a square-free polynomial with integer coefficients and without reciprocal factors. 相似文献
16.
We prove the absolute continuity of the spectrum of the Schrödinger operator in
,
, with periodic (with a common period lattice
) scalar
and vector
potentials for which either
,
, or the Fourier series of the vector potential
converges absolutely,
, where
is an elementary cell of the lattice
,
for
, and
for
, and the value of
is sufficiently small, where
and
otherwise,
, and
. 相似文献
17.
Frank Filbir Roland Girgensohn Anu Saxena Ajit Iqbal Singh Ryszard Szwarc 《Journal of Computational Analysis and Applications》2000,2(2):177-213
For an orthogonal polynomial system
and a sequence
of nonzero numbers,let
be the linear operator defined on the linear spaceof all polynomials via
for all
.We investigate conditions on
and
under which
can simultaneously preserve the orthogonality ofdifferent polynomial systems. As an application, we get that for
, a generalized Laguerre polynomial system, no
can simultaneously preserve the orthogonality of twoadditional Laguerre systems,
and
, where
and
. On the other hand, for
,the Chebyshev polynomial system and
,
simultaneously preserves the orthogonality of uncountablymany kernel polynomial systems associated with p. We study manyother examples of this type. 相似文献
18.
H. Fiedler 《Numerische Mathematik》1987,51(5):571-581
Summary Interpolatory quadrature formulae consist in replacing
by
wherep
f
denotes the interpolating polynomial off with respect to a certain knot setX. The remainder
may in many cases be written as
wherem=n resp. (n+1) forn even and odd, respectively. We determine the asymptotic behaviour of the Peano kernelP
X
(t) forn for the quadrature formulae of Filippi, Polya and Clenshaw-Curtis. 相似文献
19.
D. F. Kuznetsov 《Journal of Mathematical Sciences》2002,109(6):2148-2165
An expansion of multiple Stratonovich stochastic integrals of multiplicity
, into multiple series of products of Gaussian random variables is obtained. The coefficients of this expansion are the coefficients of multiple Fourier-series expansion of a function of several variables relative to a complete orthonormal system in the space
. The convergence in mean of order
, is established. Some expansions of multiple Stratonovich stochastic integrals with the help of polynomial and trigonometric systems are considered. Bibliography: 8 titles. 相似文献
20.
Vratislava Mošová 《Applications of Mathematics》2000,45(6):401-410
As a measure of deformation we can take the difference D
- R, where D
is the deformation gradient of the mapping
and R is the deformation gradient of the mapping
, which represents some proper rigid motion. In this article, the norm
is estimated by means of the scalar measure e(
) of nonlinear strain. First, the estimates are given for a deformation
W
1,p() satisfying the condition . Then we deduce the estimate in the case that
(x) is a bi-Lipschitzian deformation and . 相似文献
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