where Hom(π1(X), G) denotes the space of all group homomorphisms from the fundamental group π1(X) into G, and G acts on this space by conjugation. Let φ : π1(X) → G be a homomorphism, and let [φ] denote the corresponding point of LocG(X). Note that φ defines a π1(X)-module structure on g via the adjoint representation of G. Let us denote this π1(X)-module by gφ, and let Eφ denote the associated...

Every continuous map X → S defines, by composition, a homomorphism between the corresponding algebras of real-valued continuous functions C(S) → C(X). This paper deals with algebraic properties of the homomorphism C(S)→ C(X) in relation to topological properties of the map X → S. The main result of the paper states that a continuous map X → S between topological manifolds is a finite (branched)...

In this paper we determine the structure of the natural Ũ(n, n) module Ωp,q(l) which is the Howe quotient corresponding to the determinant character det of U(p, q). We first give a description of the tempered distributions on Mp+q,n(C) which transform according to the character det−l under the linear action of U(p, q). We then show that after tensoring with a character, Ωp,q(l) can be embedded ...

Let G be a connected reductive group G over an algebraically closed field k of prime characteristic p, and g = Lie(G). In this paper, we study modular representations of the reductive Lie algebra g with p-character χ of standard Levi-form associated with an index subset I of simple roots. With aid of support variety theory we prove a theorem that a Uχ(g)-module is projective if and only if it i...

(c) μ(rs,m) = μ(r, μ(s,m)) (d) if 1 ∈ R, then μ(1,m) = m. We shall usually omit the notation of μ and simply write r ·m for μ(r,m). Thus axiom (c) would be written (rs) ·m = r · (s ·m), etc. Exercise 1. We denote by EndGrp(M) the set of group endomorphisms of M : An element φ ∈ EndGrp(M) is a group homomorphism φ : M → M . EndGrp(M) is naturally a ring, with addition and multiplication defined ...

Let G be the planar Galilean conformal algebra and G˜ its universal central extension. Then (resp. G˜) admits a triangular decomposition: G=G+?G0?G? G˜=G˜+?G˜0?G˜?). In this paper, we study generic Whittaker G-modules G˜-modules) of type ?, where ?:G+?G˜+?C is Lie homomorphism. We classify isomorphism classes modules. Moreover, show that module ? simple if only nonsingular. For nonsingular case...

Let [Formula: see text] be a commutative Noetherian ring. For finitely generated text]-module text], Northcott introduced the reducibility index of which is number submodules appearing in an irredundant irreducible decomposition submodule text]. On other hand, for Artinian Macdonald proved that sum-irreducible representation does not depend on choice representation. This called sum-reducibility...

This paper presents a solution for the license plate recognition problem in residential community administrations in China. License plate images are pre-processed through gradation, middle value filters and edge detection. In the license plate localization module the number of edge points, the length of license plate area and the number of each line of edge points are used for localization. In ...

We study testing properties of functions on finite groups. First we consider functions of the form f : G → C, where G is a finite group. We show that conjugate invariance, homomorphism, and the property of being proportional to an irreducible character is testable with a constant number of queries to f , where a character is a crucial notion in representation theory. Our proof relies on represe...

We describe the structure of a Verma module with a generic highest weight at the critical level over a symmetrizable affine Lie superalgebra ĝ 6= A(2k, 2l). We obtain the character formula for a simple module with a generic highest weight at the critical level conjectured by V. G. Kac and D. A. Kazhdan.