Unitary representations of the Cherednik algebra: V^*-homology

2020/08/10 by Fishel, Susanna, Griffeth, Stephen, Manosalva, Elizabeth
#05E05 #14N20 #16S80 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2008.04412

Abstract

We give a non-negative combinatorial formula, in terms of Littlewood-Richardson numbers, for the homology of the unitary representations of the cyclotomic rational Cherednik algebra, and as a consequence, for the graded Betti numbers for the ideals of a class of subspace arrangements arising from the reflection arrangements of complex reflection groups.

Related

• Unitary representations of cyclotomic rational Cherednik algebras
• Subspace arrangements and Cherednik algebras
• On some representations of the rational Cherednik algeba
• Representations of Cherednik Algebras Associated to Symmetric and Dihedral Groups in Positive Characteristic
• Representations of the rational Cherednik algebra H_t,c(S₃,\h) in positive characteristic