Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20G05

Retrieve articles in all journals with MSC: 20G05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-1035211-6
PII: S 0002-9947(1990)1035211-6
Article copyright: © Copyright 1990 American Mathematical Society