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Hecke Algebras of TypeDnat Roots of Unity

✍ Scribed by Jun Hu; Jian-pan Wang


Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
209 KB
Volume
212
Category
Article
ISSN
0021-8693

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Iwahori–Hecke Algebras of TypeAat Roots
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We thank the referee for an exceptionally careful reading of a previous version of this paper and for pointing the way towards several improvements in the exposition. H. W. was supported in part by WSF Grant DMS 9706839. 694

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We begin by constructing Hecke algebras for arbitrary finite regular monoids M. We then show that the semisimplicity of the complex monoid algebra ‫ރ‬ M is equivalent to the semisimplicity of the associated Hecke algebras and a condition on induced group characters. We apply these results to finite

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Hecke algebras are usually defined algebraically, via generators and relations. We give a new algebra-geometric construction of affine and double-affine Hecke algebras (the former is known as the Iwahori Hecke algebra, and the latter was introduced by Cherednik) in terms of residues. More generally,