Mathematics – Representation Theory
Scientific paper
2011-06-25
Mathematics
Representation Theory
20 pages
Scientific paper
The goal of this paper is to classify the unitary irreducible modules in category O for the rational Cherednik algebras of type G(r,1,n). As a first step, we classify those irreducibles in O that are diagonalizable with respect to a commutative subalgebra introduced by Dunkl and Opdam. As a byproduct, we obtain combinatorial character formulas for many irreducible modules in category O, in terms of certain column-strict tableaux.
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