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One-W-type Modules for Rational Cherednik Algebra and Cuspidal Two-sided Cells
by Dan Ciubotaru

Vol. 13 No. 1 (2018) P.1~P.29
 DOI: https://doi.org/10.21915/BIMAS.2018101 10.21915/BIMAS.2018101

ABSTRACT

We classify the simple modules for the rational Cherednik algebra $\bf{H_{0,c}}$ 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, in the sense of Bellamy, and the cuspidal two-sided cells.

KEYWORDS
Rational Cherednik algebra, affine Hecke algebra, cells, Weyl group, Dirac cohomology.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 20C08, 20F55.

MILESTONES