Commentarii Mathematici Helvetici


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Volume 78, Issue 2, 2003, pp. 308–334
DOI: 10.1007/s000140300013

Classification of graded Hecke algebras for complex reflection groups

Arun Ram (1) and A. V. Shepler (2)

(1) Department of Mathematics and Statistics, University of Melbourne, 480 Lincoln Drive, 3010, PARKVILLE VIC, AUSTRALIA
(2) Department of Mathematics, University of North Texas, 408 General Academic Building, P.O. Box 311430, TX 76203-1430, DENTON, UNITED STATES

The graded Hecke algebra for a finite Weyl group is intimately related to the geome- try 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 non- trivial) 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

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