Irreducible representations of the rational Cherednik algebra associated to the Coxeter group \(H_3\).

DOI10.1016/j.jalgebra.2013.01.003zbMath1336.20005arXiv1004.2108OpenAlexW2963310595MaRDI QIDQ401949

Arjun Puranik, Martina Balagović

Publication date: 27 August 2014

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

Full work available at URL: https://arxiv.org/abs/1004.2108

zbMATH Keywords

category \(\mathcal O\)finite-dimensional representationsrational Cherednik algebrascharacters of irreducible representationsCoxeter group \(H_3\)

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)

Related Items

Parabolic degeneration of rational Cherednik algebras ⋮ On refined filtration by supports for rational Cherednik categories \(\mathcal {O}\) ⋮ Geometric representations of graded and rational Cherednik algebras

Uses Software

• Magma

Cites Work

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• Supports of irreducible spherical representations of rational Cherednik algebras of finite Coxeter groups. (With an appendix by Stephen Griffeth).
• Calogero-Moser systems and representation theory
• Finite-dimensional representations of DAHA and affine Springer fibers: the spherical case.
• Decomposition numbers for generic Iwahori-Hecke algebras of noncrystallographic type
• The Magma algebra system. I: The user language
• Cherednik algebras and differential operators on quasi-invariants.
• On the category \(\mathcal O\) for rational Cherednik algebras.
• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism.
• Double affine Hecke algebras and Macdonald's conjectures
• A remark on the irreducible characters and fake degrees of finite real reflection groups
• Parabolic induction and restriction functors for rational Cherednik algebras.
• Representations of the rational Cherednik algebras of dihedral type.
• Catalan numbers for complex reflection groups
• Unitary representations of rational Cherednik algebras
• Differential-Difference Operators Associated to Reflection Groups
• Singular Polynomials for Finite Reflection Groups
• DUNKL OPERATORS FOR COMPLEX REFLECTION GROUPS