Classification of graded Hecke algebras for complex reflection groups

  • Arun Ram

    University of Melbourne, Parkville, Australia
  • A. V. Shepler

    University of North Texas, Denton, USA


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

Cite this article

Arun Ram, A. V. Shepler, Classification of graded Hecke algebras for complex reflection groups. Comment. Math. Helv. 78 (2003), no. 2, pp. 308–334

DOI 10.1007/S000140300013