## Classification of graded Hecke algebras for complex reflection groups

Last update: 22 January 2014

## 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 $GL\left(V\right)\text{.}$ 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.

## Notes and references

This is a typed version of Classification of graded Hecke algebras for complex reflection groups by Arun Ram and Anne V. Shepler.

Research of the first author supported in part by the National Security Agency and by EPSRC Grant GR K99015 at the Newton Institute for Mathematical Sciences. Research of the second author supported in part by National Science Foundation grant DMS-9971099.