Asymptotic Hecke algebras and involutions
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conm610-12156.pdf
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209.71 KB
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Author(s)
Lusztig, George
Date Issued
2014
Journal
Perspectives in Representation Theory
Publisher
American Mathematical Society
Citation
Lusztig, G. “Asymptotic Hecke Algebras and Involutions.” Contemporary Mathematics (2014): 267–278 © 2014 American Mathematical Society
Version
Final published version
Abstract
In [11], a Hecke algebra module structure on a vector space spanned by
the involutions in a Weyl group was defined and studied. In this paper this study is continued by relating it to the asymptotic Hecke algebra introduced in [6]. In particular we define a module over the asymptotic Hecke algebra which is spanned by the involutions in the Weyl group. We present a conjecture relating this module to equivariant vector bundles with respect to a group action on a finite set. This gives an explanation (not a proof) of a result of Kottwitz [3] in the case of classical Weyl groups, see 2.5. We also present a conjecture which realizes the module in [11] terms of an ideal in the Hecke algebra generated by a single element, see 3.4.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1090/conm/610/12156
