Affine Hecke algebras, cyclotomic Hecke algebras and Clifford theory

Details Affine Hecke algebras, cyclotomic Hecke algebras and Clifford theory Affine Hecke algebras, cyclotomic Hecke algebras and Clifford theory

2004-01-23

arxiv.org/abs/math/0401322v2

Published in A tribute to C.S. Seshadri: Perspectives in Geometry and Representation theory, V. Lakshimibai et al eds., Hindus

Mathematics

Representation Theory

Scientific paper

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 H_{r,p,n}, can be obtained, in all cases, from the affine Hecke algebra of type A. The Young tableaux theory was extended to affine Hecke algebras (of general Lie type) in recent work of A. Ram. We also show how (in general Lie type) the representations of general affine Hecke algebras can be constructed from the representations of simply connected affine Hecke algebras by using an extended form of Clifford theory. This extension of Clifford theory is given in the Appendix.

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