Generalized graded Hecke algebra for complex reflection group of type G(r,1,n)

Details Generalized graded Hecke algebra for complex reflection group of type G(r,1,n) Generalized graded Hecke algebra for complex reflection group of type G(r,1,n)

2006-05-15

arxiv.org/abs/math/0605410v2

Mathematics

Representation Theory

12 pages

Scientific paper

We study the representation theory of a generalized graded Hecke algebra
associated to a complex reflection group of type G(r,1,n), defined by Ram and
Shepler. We use a realization of this algebra in the corresponding symplectic
reflection algebra to prove a PBW theorem. We define principal series modules
and prove an irreducibility criterion for them.

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