Classification of graded Hecke algebras for complex reflection groups |
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Authors: | A Ram A V Shepler |
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Institution: | (1) Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA , US;(2) Department of Mathematics, University of North Texas, Denton, TX 76203, USA , US |
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Abstract: | The graded Hecke algebra for a finite Weyl group is intimately related to the geometry of the Springer correspondence. A
construction of Drinfeld produces an analogue of a graded Hecke algebra for any finite subgroup of GL(V). This paper classifies all the algebras obtained by applying Drinfeld's construction to complex reflection groups. By giving
explicit (though nontrivial) isomorphisms, we show that the graded Hecke algebras for finite real reflection groups constructed
by Lusztig are all isomorphic to algebras obtained by Drinfeld's construction. The classification shows that there exist
algebras obtained from Drinfeld's construction which are not graded Hecke algebras as defined by Lusztig for real as well
as complex reflection groups.
Received: July 25, 2001 |
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Keywords: | , Reflection group, Coxeter group, Weyl group, affine Hecke algebra, Iwahori-Hecke algebra, representation theory,,,,,,graded Hecke algebra, |
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