One-W-type modules for rational Cherednik algebra and cuspidal two-sided cells

2015/03/26 by Dan Ciubotaru, Ciubotaru, Dan · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1503.07890

16 pages; added references, corrected misprints

openalex publication_date 2015/03/26 · arxiv created 2015/03/30 · arxiv updated 2015/03/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We classify the simple modules for the rational Cherednik algebra that are irreducible when restricted to W, in the case when W is a finite Weyl group. The classification turns out to be closely related to the cuspidal two-sided cells in the sense of Lusztig. We compute the Dirac cohomology of these modules and use the tools of Dirac theory to find nontrivial relations between the cuspidal Calogero-Moser cells and the cuspidal two-sided cells.

Cited by

• Non-homogeneous Koszul duality in representation theory
• Dirac cohomology for symplectic reflection algebras

Related

• Cuspidal representations of rational Cherednik algebras at t=0
• Unitary representations of cyclotomic rational Cherednik algebras
• Parabolic degeneration of rational Cherednik algebras
• Supports of simple modules in cyclotomic Cherednik categories O
• Representations of the rational Cherednik algebras of dihedral type