Action of longest element on a Hecke algebra cell module

G. Lusztig

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arXiv · 1406.0452

Action of longest element on a Hecke algebra cell module

G. Lusztig

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Abstract

By a result of Mathas, the basis element T_{w_0} of the Hecke algebra of a finite Coxeter group acts in the canonical basis of a cell module as a permutation matrix times plus or minus a power of v. We generalize this result to the unequal parameter case,. We also show that the image of T_{w_0} in the corresponding asymptotic Hecke algebra is given by a simple formula.

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G. Lusztig. 2015-06-27. Action of longest element on a Hecke algebra cell module. https://arxiv.org/abs/1406.0452

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