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

Abstract

We give a non-negative combinatorial formula, in terms of Littlewood-Richardson numbers, for the $$V^*$$ -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.