Unitary representations of cyclotomic rational Cherednik algebras

JOURNAL OF ALGEBRA

卷:512

Article

Griffeth, Stephen¹ 

[1] Univ Talca, Inst Matemat & Fis, Talca, Chile

关键词: Unitary representations;    Cherednik algebras;    Character formulas;   

DOI  :  10.1016/j.jalgebra.2018.07.011

来源: Elsevier

【 摘 要 】

We classify the irreducible unitary modules in category O-c 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 lambda(center dot) of n, the closed semi-linear set of parameters c for which the contravariant form on the irreducible representation L-c(lambda(center dot)) 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free