here l(w) is the length of w In the case where Wis a Weyl group and q is specialized to a fixed prime power, | ~ can be interpreted as the algebra of intertwining operators of the space of functions on the flag manifold of the corresponding finite Chevalley group G(Fq) (see [loc cit, Ex 24]) Therefore, the problem of decomposing this space of functions into irreducible representations of G(Fq) is equivalent to the problem of decomposing the regular representation o f ~ | (12 It is known that, in this case, | is isomorphic to the group algebra of W; however, in general, this isomorphism cannot be defined without introducing a square root of q (see [1]) It is therefore, natural to extend the ground ring of ~ as follows For any Coxeter group (W, S) we define the Hecke algebra ~ to be J{' | A, where A is the ring of Laurent polynomials with integral coefficients in the indeterminate ql/2 Our purpose is to construct representations oL,Uf endowed with a special basis They will be defined in terms of certain graphs We define a W-graph to be a set of vertices X, with a set Y of edges (an edge is a subset of X consisting of two elements) together with two additional data: for each vertex xeX , we are given a subset I x of S and, for each ordered pair of vertices y, x such that {y, x} e Y, we are given an integer p(y, x) +0 These data are subject to the requirements (10a), (10b) below Let E be

Representations of Coxeter Groups and Hecke Algebras.

We study for g=g[(N+1) the structure and representations of the algebra Ŭ(g), a q-analogue of the universal enveloping algebra U(g). Applying the result, we construct trigonometric solutions of the Yang-Baxter equation associated with higher representations of g.

A q-analogue of U(g[(N+1)), Hecke algebra, and the Yang-Baxter equation

Propriétés galoisiennes des points d'ordre fini des courbes elliptiques

A linear algebraic group over an algebraically closed field k is a subgroup of a group GL n (k) of invertible n × n-matrices with entries in k, whose elements are precisely the solutions of a set of polynomial equations in the matrix coordinates. The present article contains a review of the theory of linear algebraic groups.

Linear Algebraic Groups

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Modular curves and the Eisenstein ideal

Notation Background from Group Theory Representations and Modules Algebraic Number Theory Semi-Simple Rings and Group Algebras Group Characters Induced Characters Induced Representation Non-Semi-Simple Rings Frobenius Algebras Splitting Fields and Separable Algebras Integral Representations Modular Representations Index

Representation Theory of Finite Groups and Associative Algebras

Methods of Representation Theory

Group Representations and Character Theory. Introduction to Modular Representations. Integral Representations: Orders and Lattices. Local and Global Theory of Integral Representations. Bibliography. Index.

Methods of representation theory--with applications to finite groups and orders

Seminar on Algebraic Groups and Related Finite Groups

http://library.um.ac.id/free-contents/downloadpdf.php/buku/methods-of-representation-theory-with-applications-to-finite-groups-and-orders-charles-w-curtis-irving-reiner-12613.pdf

Charles W. Curtis

Papers

Representation Theory of Finite Groups and Associative Algebras

Methods of Representation Theory

Methods of representation theory--with applications to finite groups and orders

Seminar on Algebraic Groups and Related Finite Groups

Methods of representation theory : with applications to finite groups and orders / Charles W. Curtis, Irving Reiner