Asymptotic Hecke algebras and involutions
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...
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| Format: | Article |
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American Mathematical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/115861 https://orcid.org/0000-0001-9414-6892 |
| Summary: | 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. |
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