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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On matrix coefficients of the reflection representation


Authors: J. Matthew Douglass and Brad Shelton
Journal: Proc. Amer. Math. Soc. 105 (1989), 62-65
MSC: Primary 17B35; Secondary 20C30, 20G05
MathSciNet review: 930242
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Abstract: We answer in the affirmative a question of Lusztig on the signs of certain matrix coefficients for the reflection representation of the Hecke algebra of a finite Weyl group. In the action of the Weyl group on the associated root system, the coefficients of the action of an element on a root are all of the same sign. It is shown that an appropriate generalization of this property holds for the reflection representation.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0930242-3
PII: S 0002-9939(1989)0930242-3
Article copyright: © Copyright 1989 American Mathematical Society