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A new basis for the representation ring of a Weyl group

Author: G. Lusztig
Journal: Represent. Theory 23 (2019), 439-461
MSC (2010): Primary 20G99
Published electronically: October 23, 2019
MathSciNet review: 4021825
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Abstract: Let $W$ be a Weyl group. In this paper we define a new basis for the Grothendieck group of representations of $W$. This basis contains on the one hand the special representations of $W$ and on the other hand the representations of $W$ carried by the left cells of $W$. We show that the representations in the new basis have a certain bipositivity property.

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Additional Information

G. Lusztig
Affiliation: Department of Mathematics, Room 2-365, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
MR Author ID: 117100

Received by editor(s): January 1, 2400
Published electronically: October 23, 2019
Additional Notes: The author was supported by NSF grant DMS-1566618.
Article copyright: © Copyright 2019 American Mathematical Society