STABILITY OF CERTAIN RINGS OF HIGHEST WEIGHT VECTORS

51. IntroductionLet Cm'" be the space of complex m x n matrices, P(Cm)") be the algebra of complexpolynomials on Cd'~. Let GLm(C) x GL.(C) act on P(Cm,") as the following:(gi, gZ)f(x) ~ f(g,'xg,),where x E Cat", (gi, g2) E GLm x GL., f E P(Cm'"). This action induces an action of thesubgroup Of x GL. on P(Cm)") by restriction.Let G be a complex reductive algebraic group, (V, p) be a rational representation of G.Let B = TU be a Borel subgroup of G, where T is a majximal torns of …     

On an asymptotic behavior of elements of order in irreducible representations of the classical algebraic groups with large enough highest weights

The behavior of the images of a fixed element of order in irreducible representations of a classical algebraic group in characteristic with highest weights large enough with respect to and this element is investigated. More precisely, let be a classical algebraic group of rank over an algebraically closed field of characteristic 2$">. Assume that an element of order is conjugate to that of an algebraic group of the same type and rank naturally embedded into . Next, an integer function on the set of dominant weights of and a constant that depend only upon , and a polynomial of degree one are defined. It is proved that the image of in the irreducible representation of with highest weight contains more than Jordan blocks of size if and are not too small and .

     

Free Resolution Invariants for Finite Groups

Given a finite group G and a G-free resolution F _* of Z, then d _G (Im(F _m+1F _m ))–(–1) ^m–i d _G (F _i ) is almost always an invariant of G.     

The connection between self‐associated two‐dimensional vector functionals and third degree forms

We deal with the 2‐orthogonal, 2‐symmetric self‐associated sequence (2‐orthogonal Tchebychev polynomials) and its cubic components. We prove that all the forms (linear functionals) arising are third degree forms. Therefore, an introduction to third degree forms is provided. We look for the connection between these components which are 2‐orthogonal with respect to the functional vector ^t(w₀{^μ},w₁ ^μ) and orthogonal sequences with respect to w₀ ^μ, μ=0,1,2. Associated forms w₀ ^μ)¹) and their inverse w₀ ^μ)^-1 are also studied through the symmetrized w₀}₀ ^μ, μ=0,1,2. Further, we give integral representations for some of these forms. This revised version was published online in June 2006 with corrections to the Cover Date.     

Superstochastic matrices and magic Markov chains

A brief account of the conceptual formulation of the two entities in this paper’s title, plus an initial preliminary investigation of some of their mathematical properties, is given.     

Shearlet coorbit spaces and associated Banach frames

In this paper, we study the relationships of the newly developed continuous shearlet transform with the coorbit space theory. It turns out that all the conditions that are needed to apply the coorbit space theory can indeed be satisfied for the shearlet group. Consequently, we establish new families of smoothness spaces, the shearlet coorbit spaces. Moreover, our approach yields Banach frames for these spaces in a quite natural way. We also study the approximation power of best n-term approximation schemes and present some first numerical experiments.     

关于自守型式的Langlands函子性

本文系该著者有关自守型式的Langlands函子性的演讲稿的细述及扩充文稿.特别强调了与该著者的近期工作相关的课题.     

Colour symmetry double point groups

Thirty four distinct composition series arising out of the 32 crystallographic double point groups are employed to re-derive in a simple and elegant fashion all the 169 distinct colour symmetry groups generated by the 32 double point groups, exploiting the idea of colour generators. The advantage of the method employed and some possible applications of these colour groups are discussed. The resulting colour groups are tabulated.     

Functional Representations of Lawson Monads

We introduce a class of Lawson monads and show that these monads have a functional representation. A characterisation of such a representation for the inclusion hyperspace monad is given.