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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Cells and the reflection representation of Weyl groups and Hecke algebras

Author: J. Matthew Douglass
Journal: Trans. Amer. Math. Soc. 318 (1990), 373-399
MSC: Primary 20G05
MathSciNet review: 1035211
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Abstract: Let $ \mathcal{H}$ be the generic algebra of the finite crystallographic Coxeter group $ W$, defined over the ring $ \mathbb{Q}[{u^{1/2}},{u^{ - 1/2}}]$. First, the two-sided cell corresponding to the reflection representation of $ \mathcal{H}$ is shown to consist of the nonidentity elements of $ W$ having a unique reduced expression. Next, the matrix entries of this representation are computed in terms of certain Kazhdan-Lusztig polynomials. Finally, the Kazhdan-Lusztig polynomials just mentioned are described in case $ W$ is of type $ {{\text{A}}_{l - 1}}$ or $ {{\text{B}}_l}$.

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Article copyright: © Copyright 1990 American Mathematical Society

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