Multiplicity matrices for the affine graded Hecke algebra

Details Multiplicity matrices for the affine graded Hecke algebra Multiplicity matrices for the affine graded Hecke algebra

2008-01-09

arxiv.org/abs/0801.1526v1

Mathematics

Representation Theory

30 pages

Scientific paper

In this paper, we look at the problem of determining the composition factors for the affine graded Hecke algebra via the computation of Kazhdan-Lusztig type polynomials. We review the algorithms of \cite{L1,L2}, and use them in particular to compute, at every real central character which admits tempered modules, the geometric parameterization, the Kazhdan-Lusztig polynomials, the composition series, and the Iwahori-Matsumoto involution for the representations with Iwahori fixed vectors of the split $p$-adic groups of type $G_2$ and $F_4$.

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