Classification of graded Hecke algebras for complex reflection groups
By Arun Ram, Anne V. Shepler. 2002
89 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/285fbde39674cdf53bafcbd06bbf1d6d63049fed
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In Algebra and Number Theory
In Geometry and Topology
- Stephen Griffeth
- I. Gordon
- V. Ginzburg
- Pavel Etingof
- I. Losev
- Charles F. Dunkl
- J. T. Stafford
- E. Gorsky
In Mathematical Physics
- Stephen Griffeth
- I. Gordon
- V. Ginzburg
- Pavel Etingof
- Charles F. Dunkl
- J. T. Stafford
- E. Gorsky
- I. Losev
Citations in the corpus
- Orthogonal functions generalizing Jack polynomials (2007, methodology): “The PBW theorem (see (8), (12), (28), and (19)) for H asserts that as F -vector spaces, (4.”
- Group actions on algebras and the graded Lie structure of Hochschild cohomology (2009, unknown): “See [16, 17] for basic definitions.”
- Symplectic reflection algebras (2007, methodology): “In the symplectic case this was rediscovered by Etingof and Ginzburg as above, and Drinfeld’s general case was described in detail by Ram–Shepler, [124].”