REPRESENTATIONS OF AFFINE HECKE ALGEBRAS OF TYPE G2

doi:10.1016/S0252-9602(09)60050-3

Abstract

Abstract:

Let k be a field and q a nonzero element in k such that the square roots of q are in k. We use H_qto denote an affine Hecke algebra over k of type G₂with parameter q. The purpose of this paper is to study representations of H_q by using based rings of two-sided cells of an affine Weyl group W of type G₂. We shall give the classification of irreducible representations of H_q. We also remark that a calculation in [11] actually shows that Theorem 2 in [1] needs a modification, a fact is known to Grojnowski and Tanisaki long time ago. In this paper we also show an interesting relation between H_q and an Hecke algebra corresponding to a certain Coxeter group. Apparently the idea in this paper works for all affine Weyl groups, but that is the theme of another paper.

Key words: representation, affine Hecke algebra, affine Weyl groups, Hecke algebra

CLC Number:

20C08

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XI Na-Hua. REPRESENTATIONS OF AFFINE HECKE ALGEBRAS OF TYPE G₂[J].Acta mathematica scientia,Series B, 2009, 29(3): 515-526.

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References

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