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

2006/05/15 by C. Dezelee, Dezelee, C.
Mathematics · #16Sxx #17Bxx #33Dxx #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Finite Group Theory Research #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0605410

openalex publication_date 2006/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Classification of graded Hecke algebras for complex reflection groups
• Generic Hecke Algebras for Monomial Groups
• On the Irreducibility of the Complex Specialization of the Representation of The Hecke Algebra of the Complex Reflection Group G₇
• The many graded cellular bases of Hecke algebras
• Unitary representations of Hecke algebras of complex reflection groups