Unitary representations of cyclotomic rational Cherednik algebras

We classify the irreducible unitary modules in category Oc 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 λ• of n, the closed semi-linear...

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Bibliographic Details
Published inJournal of algebra Vol. 512; pp. 310 - 356
Main Author Griffeth, Stephen
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.10.2018
Subjects
Character formulas
Cherednik algebras
Unitary representations
Unitary representations
Character formulas
Cherednik algebras
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Summary:We classify the irreducible unitary modules in category Oc 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 λ• of n, the closed semi-linear set of parameters c for which the contravariant form on the irreducible representation Lc(λ•) 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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2018.07.011