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1.
Let W (z) and M(z) be v-valued and k-valued algebroidal functions respectively,(θ) be a b-cluster line of order ∞ (or ρ(r)) of W (z) (or M(z)).It is shown that W (z) ≡ M(z) provided E(a j ,W (z)) = E(a j ,M(z)) (j = 1,...,2v + 2k + 1) holds in the angular domain Ω(θ- δ,θ + δ),where b,a j (j = 1,...,2v + 2k + 1) are complex constants.The same results are obtained for the case that (θ) is a Borel direction of order ∞ (or ρ(r)) of W (z) (or M(z)). 相似文献
2.
ON Δ-GOOD MODULE CATEGORIES OF QUASI-HEREDITARY ALGEBRAS 总被引:2,自引:0,他引:2
ONΔ┐GOODMODULECATEGORIESOFQUASI┐HEREDITARYALGEBRAS**DENGBANGMING*XICHANGCHANG*ManuscriptreceivedJune12,1995.RevisedMay3,1996.... 相似文献
3.
ON Δ-GOOD MODULE CATEGORIES OF QUASI-HEREDITARY ALGEBRAS 总被引:2,自引:0,他引:2
A useful reduction is presented to determine the finiteness of △-good module category F(△)of a quasi-heredltary algebra. As an application of the reduction, the f(△)-finitenetess of quasi-hereditary M-twisted double incidence algebras of posets is discussed. In particular, a complete classification of F(△)-finite M-twisted double incidence algebras is given in case the posets are linearly ordered. 相似文献
4.
Shen Guangyu 《数学年刊B辑(英文版)》1988,9(4):404-417
Over a field of characteristic$\[ \ne 2\]$, 3, all irreducible positive and negative graded modules
of simple Lie algebras $\[L(n)\]$ and $\[L(n,m)\]$ of Cartan typs $\[W,S\]$, and H are determined.
Further, all irreducible positive and negative filtered modules of $\[L(n,m)\]$ are determined.For $\[L(n)\]$, every irreducible negative filtered module is a negative graded module, but there exist irreducible positive filtered modules which are not graded. 相似文献
5.
Let G be a finite group and K a field of characteristic zero.It is well-known that if K is a splitting field for G,then G is abelian if and only if any irreducible representation of G has degree 1.In this paper,we generalize this result to the case that K is an arbitrary field of characteristic zero(that is,K need not be a splitting field for G),and we also obtain the orthogonality relations of irreducible K-characters of G in this case.Our results generalize some well-known theorems. 相似文献
6.
ESSENTIALLY NORMAL + SMALL COMPACT = STRONGLY IRREDUCIBLE 总被引:3,自引:0,他引:3
Given an essentially normal operator T with connected spectrum and ind(λ -- T) > 0 for λ in pF(T) ∩ σ(T), and a positive number ε, the authors show that there exists a compact K with ‖K‖< ε such that T + K is strongly irreducible. 相似文献
7.
Let $G_M$ be either the orthogonal group $O_M$ or the
symplectic group $Sp_M$ over the complex field; in the latter case
the non-negative integer $M$ has to be even. Classically, the
irreducible polynomial representations of the group $G_M$ are
labeled by partitions $\mu=(\mu_{1},\mu_{2},\,\ldots)$
such that $\mu^{\prime}_1+\mu^{\prime}_2\le M$ in the case $G_M=O_M$, or
$2\mu^{\prime}_1\le M$ in the case $G_M=Sp_M$. Here
$\mu^{\prime}=(\mu^{\prime}_{1},\mu^{\prime}_{2},\,\ldots)$ is the partition
conjugate to $\mu$. Let $W_\mu$ be the irreducible polynomial
representation of the group $G_M$ corresponding to $\mu$.
Regard $G_N\times G_M$ as a subgroup of $G_{N+M}$.
Then take any irreducible polynomial representation
$W_\lambda$ of the group $G_{N+M}$.
The vector space
$W_{\lambda}(\mu)={\rm Hom}_{\,G_M}( W_\mu, W_\lambda)$
comes with a natural action of the group $G_N$.
Put $n=\lambda_1-\mu_1+\lambda_2-\mu_2+\ldots\,$.
In this article, for any standard Young tableau $\varOmega$ of
skew shape $\lm$ we give a realization of $W_{\lambda}(\mu)$
as a subspace in the $n$-fold tensor product
$(\mathbb{C}^N)^{\bigotimes n}$, compatible with the action of the group $G_N$.
This subspace is determined as the image of a certain linear operator
$F_\varOmega (M)$ on $(\mathbb{C}^N)^{\bigotimes n}$, given by an explicit formula.
When $M=0$ and $W_{\lambda}(\mu)=W_\lambda$ is an irreducible representation of
the group $G_N$, we recover the classical realization of $W_\lambda$
as a subspace in the space of all traceless tensors in $(\mathbb{C}^N)^{\bigotimes n}$.
Then the operator $F_\varOmega\(0)$ may be regarded as the analogue
for $G_N$ of the Young symmetrizer, corresponding to the
standard tableau $\varOmega$ of shape $\lambda$.
This symmetrizer is a certain linear operator on
$\CNn$$(\mathbb{C}^N)^{\bigotimes n} $ with the image equivalent to the irreducible
polynomial representation of the complex general linear group
$GL_N$, corresponding to the partition $\lambda$. Even in the case
$M=0$, our formula for the operator $F_\varOmega(M)$ is new.
Our results are applications of the representation
theory of the twisted Yangian, corresponding to the
subgroup $G_N$ of $GL_N$. This twisted Yangian
is a certain one-sided coideal subalgebra of the Yangian corresponding
to $GL_N$. In particular, $F_\varOmega(M)$ is an intertwining
operator between certain representations of the twisted Yangian
in $(\mathbb{C}^N)^{\bigotimes n}$. 相似文献
8.
In this paper, let m, n be two fixed positive integers and M be a right R-module, we define (m, n)-M-flat modules and (m, n)-coherent modules. A right R-module F is called (m, n)-M-flat if every homomorphism from an (n, m)-presented right R-module into F factors through a module in addM. A left S-module M is called an (m, n)-coherent module if MR is finitely presented, and for any (n, m)-presented right R-module K, Hom(K, M) is a finitely generated left S-module, where S = End(MR). We mainly characterize (m, n)-coherent modules in terms of preenvelopes (which are monomorphism or epimorphism) of modules. Some properties of (m, n)-coherent rings and coherent rings are obtained as corollaries. 相似文献
9.
We prove that a well-distributed subset of ${\Bbb R}^2$
can have a distance set $\Delta$ with $\#(\Delta\cap [0,N])\leq
CN^{3/2-\epsilon}$ only if the distance is induced by a polygon
$K$. Furthermore, if the above estimate holds with
$\epsilon=\frac12$, then $K$ can have only finitely many sides. 相似文献
10.
Vladimir Mazorchuk 《Compositio Mathematica》1999,115(1):21-35
We constuct and investigate a structure of Verma-like modules over generalized Witt algebras. We also prove Futorny-like theorem for irreducible weight modlues whose dimensions of the weight spaces are uniformly bounded. 相似文献
11.
First, the authors give a Grbner-Shirshov basis of the finite-dimensional irreducible module Vq(λ) of the Drinfeld-Jimbo quantum group U_q(G_2) by using the double free module method and the known Grbner-Shirshov basis of U_q(G_2). Then, by specializing a suitable version of U_q(G_2) at q = 1, they get a Grbner-Shirshov basis of the universal enveloping algebra U(G_2) of the simple Lie algebra of type G_2 and the finite-dimensional irreducible U(G_2)-module V(λ). 相似文献
12.
Cellular algebras 总被引:4,自引:0,他引:4
13.
The authors consider the irreducibility of the Cowen-Douglas
operator $T$. It is proved that $T$ is irreducible iff the unital $C^*$-algebra
generated by some non-zero blocks in the decomposition of $T$ with respect to
$\bigoplus^\infty_{n=0}\limits(\Ker T^{n+1}\ominus\Ker T^n)$ is
$\text{M}_n(\Bbb C).$ 相似文献
14.
Christian Buchta 《Discrete and Computational Geometry》2005,33(1):125-142
Denote by $K_n$ the convex hull of $n$ independent random points
distributed uniformly in a convex body $K$ in $\R^d$, by $V_n$ the volume of
$K_n$, by $D_n$ the volume of $K\backslash K_n$, and by $N_n$ the number of
vertices of $K_n$. A well-known identity due to Efron relates the expected
volume ${\it ED}_n$---and thus ${\it EV}_n$---to the expected
number ${\it EN}_{n+1}$. This
identity is extended from expected values to higher moments.
The planar case of the arising identity for the variances provides in a simple
way the corrected version of a central limit theorem for $D_n$ by Cabo and
Groeneboom ($K$ being a convex polygon) and an improvement of a central limit
theorem for $D_n$ by Hsing ($K$ being a circular disk). Estimates of $\var D_n$
($K$ being a two-dimensional smooth convex body) and $\var N_n$ ($K$ being a
$d$-dimensional smooth convex body, $d\geq 4$) are obtained.
The identity for moments of arbitrary order shows that the distribution of $N_n$
determines ${\it EV}_{n-1}, {\it EV}_{n-2}^2,\dots, {\it EV}_{d+1}^{n-d-1}$. Reversely it is
proved that these $n-d-1$ moments determine the distribution of $N_n$ entirely.
The resulting formula for the probability that $N_n=k\ (k=d+1,\dots , n)$
appears to be new for $k\geq d+2$ and yields an answer to a question raised by
Baryshnikov. For $k=d+1$ the formula reduces to an identity which has been
repeatedly pointed out. 相似文献
15.
Zhang Guangxiang 《数学年刊B辑(英文版)》1993,14(2):209-212
The following result is proved: Let B be a block ideal of group algebra kG over a splitting field k with characteristic p. Suppose that B has only one irreducible module L and abelian defect group D, then $\[B \simeq Ma{t_m}(kD)\]$,Where $m=Dim_kL$. This result generalizes Kukhammer''s theorem concerning the structure of block algebras with inertial indel 1. 相似文献
16.
The class of rank 3 algebras includes the Jordan algebra of a symmetric bilinear form, the trace zero elements of a Jordan algebra of degree 3, pseudo-composition algebras, certain algebras that arise in the study of Riccati differential equations, as well as many other algebras. We investigate the representations of rank 3 algebras and show under some conditions on the eigenspaces of the left multiplication operator determined by an idempotent element that the finite-dimensional irreducible representations are all one-dimensional. 相似文献
17.
Aseem Dalal & N. K. Govil 《分析论及其应用》2020,36(2):225-234
Let $p(z)=\sum^n_{v=0}a_vz^v$be a polynomial of degree $n$, $M(p,R)=:\underset{|z|=R\geq 0}{\max}|p(z)|$ and $M(p,1)=:||p||$.Then according to a well-known result of Ankeny and Rivlin [1], we have for $R\geq 1$, $$M(p,R)\leq (\frac{R^n+1}{2})||p||.$$This inequality has been sharpened by Govil [4], who proved that for $R\geq 1$, $$M(p,R)\leq (\frac{R^n+1}{2})||p||-\frac{n}{2}(\frac{||p||^2-4|a_n|^2}{||p||})\left\{\frac{(R-1||p||)}{||p||+2|a_n|}-ln(1+\frac{(R-1)||p||}{||p||+2|a_n|})\right\}.$$In this paper, we sharpen the above inequality of Govil [4], which in turn sharpens the
inequality of Ankeny and Rivlin [1]. 相似文献
18.
A finite set $N \subset \R^d$ is a {\em weak $\eps$-net} for an
$n$-point set $X\subset \R^d$ (with respect to convex sets) if $N$
intersects every convex set $K$ with $|K\,\cap\,X|\geq \eps n$. We
give an alternative, and arguably simpler, proof of the fact, first
shown by Chazelle et al., that every
point set $X$ in $\R^d$ admits a weak $\eps$-net of cardinality
$O(\eps^{-d}\polylog(1/\eps))$. Moreover, for a number of special
point sets (e.g., for points on the moment curve), our method gives
substantially better bounds. The construction
yields an algorithm to construct such weak
$\eps$-nets in time $O(n\ln(1/\eps))$. 相似文献
19.
We get the characterizations of the family of all nonnegative, subadditive,β-absolutely homogeneous and continuous functionals defined on X, when the ;3-normed space X contains an asymptotically isometric copy of l^β. Moreover, it is proved that if a closed bounded β-convex subset K of a β-normed space contains an asymptotically isometric β-basis, then K contains a closed β-convex subset C which fails the fixed point property. 相似文献
20.
Let (R,m) be a Cohen-Macaulay local ring of dimension d with infinite residue field, I an m-primary ideal and K an ideal containing I. Let J be a minimal reduction of I such that, for some positive integer k, KIn ∩ J = JKIn-1 for n ≤ k ? 1 and λ( JKKIIkk-1 ) = 1. We show that if depth G(I) ≥ d-2, then such fiber cones have almost maximal depth. We also compute, in this case, the Hilbert series of FK(I) assuming that depth G(I) ≥ d - 1. 相似文献