Generalized Graded Hecke Algebras of Types B and D

DOI10.1080/00927870600549618zbMath1105.20002OpenAlexW2152688153MaRDI QIDQ5481646

Charlotte Dezélée

Publication date: 10 August 2006

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927870600549618

zbMATH Keywords

Weyl groupsroot systemsgraded Hecke algebrasDunkl operatorsrational Cherednik algebrasprincipal series modules

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Hecke algebras and their representations (20C08) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Twisted and skew group rings, crossed products (16S35) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (3)

Unitary representations of cyclotomic rational Cherednik algebras ⋮ Quantum algebras and symplectic reflection algebras for wreath products ⋮ Dirac cohomology of the Dunkl-Opdam subalgebra via inherited Drinfeld properties

Cites Work

• Quasi-quantum groups, knots, three-manifolds, and topological field theory
• Classification of graded Hecke algebras for complex reflection groups.
• On the quotient ring by diagonal invariants.
• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism.
• Harmonic analysis for certain representations of graded Hecke algebras
• Intertwining operators for a degenerate double affine Hecke algebra and multivariable orthogonal polynomials
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