Unitary representations of cyclotomic rational Cherednik algebras

2011/06/25 by Griffeth, Stephen
#05E10 #05E15 #16S35 #16S38 #16T30 #20C30 #Combinatorics (math.CO) #FOS: Mathematics #Primary: 05E05 #Representation Theory (math.RT) #Secondary: 16D90

paper · doi:10.48550/arxiv.1106.5094

Abstract

We classify the irreducible unitary modules in category O for the rational Cherednik algebras of type G(r,1,n) and give explicit combinatorial formulas for their graded characters. More precisely, we produce a combinatorial algorithm determining, for each r-partition of n, the closed semi-linear set of parameters for which the contravariant form on the irreducible representation with the given r-partition as lowest weight is positive definite. We use this algorithm to give a closed form answer for the Cherednik algebra of the symmetric group (recovering a result of Etingof-Stoica and the author) and the Weyl groups of classical type.

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