Affine Hecke algebras, cyclotomic Hecke algebras and Clifford theory

By Arun Ram, Jacqui Ramagge. 2004

83 citations recorded by the source corpus.

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 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/be008ff391714aaad8b06b1685d831438cecacea

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In Algebra and Number Theory

1. Arun Ram
2. Stephen Griffeth
3. I. Gordon

In Geometry and Topology

1. Arun Ram
2. Stephen Griffeth
3. Aaron D. Lauda
4. I. Gordon

In Mathematical Physics

1. Arun Ram
2. Stephen Griffeth
3. I. Gordon

Citations in the corpus

• Affine Hecke algebras and generalized standard Young tableaux (2003, background): “HL in terms of the representations of � HP , see [ 30 ].”