Higher level affine Schur and Hecke algebras

Affine Hecke algebras, cyclotomic Hecke algebras and Clifford theory

We show that the Young tableaux theory and constructions of the irreducible representations of the Weyl groups of type A, B and D, Iwahori-Hecke algebras of types A, B, and D, the complex reflection groups G(r, p, n) and the corresponding cyclotomic Hecke algebras Hr,p,n, can be obtained, in all cases, from the affine Hecke algebra of type A. The Young tableaux theory was extended to affine Hec...

Generalized Double Affine Hecke Algebras of Higher Rank

Hecke group algebras as degenerate affine Hecke algebras

The Hecke group algebra H W̊ of a finite Coxeter group W̊ , as introduced by the first and last author, is obtained from W̊ by gluing appropriately its 0-Hecke algebra and its group algebra. In this paper, we give an equivalent alternative construction in the case when W̊ is the classical Weyl group associated to an affine Weyl group W . Namely, we prove that, for q not a root of unity, H W̊ is the ...

Presenting affine q-Schur algebras

We obtain a presentation of certain affine q-Schur algebras in terms of generators and relations. The presentation is obtained by adding more relations to the usual presentation of the quantized enveloping algebra of type affine gln. Our results extend and rely on the corresponding result for the q-Schur algebra of the symmetric group, which were proved by the first author and Giaquinto. Mathem...

Hecke Algebras and Schur Algebras of the Symmetric Group

These notes give a fully self{contained introduction to the (modular) representation theory of the Iwahori{Hecke algebras and the q{Schur algebras of the symmetric groups. The central aim of this work is to give a concise, but complete, and an elegant, yet quick, treatment of the classiication of the simple modules and of the blocks of these two important classes of algebras. Our approach is co...