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arXiv · 0801.1526

Multiplicity matrices for the affine graded Hecke algebra

Dan Ciubotaru
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Abstract

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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Dan Ciubotaru. 2008-01-09. Multiplicity matrices for the affine graded Hecke algebra. https://arxiv.org/abs/0801.1526

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