We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
ON REPRESENTATIONS OF RATIONAL CHEREDNIK ALGEBRAS OF COMPLEX RANK.
- Authors
AIZENBUD, INNA ENTOVA
- Abstract
We study a family of abelian categories O c,ν depending on complex parameters c, ν which are interpolations of the category O for the rational Cherednik algebra Hc(ν) of type A, where ν is a positive integer. We define the notion of a Verma object in such a category (a natural analogue of the notion of Verma module). We give some necessary conditions and some sufficient conditions for the existence of a non-trivial morphism between two such Verma objects. We also compute the character of the irreducible quotient of a Verma object for sufficiently generic values of parameters c, ν, and prove that a Verma object of infinite length exists in O c,ν only if c ∈ ℚ<0. We also show that for every c ∈ ℚ<0 there exists ν ∈ ℚ<0 such that there exists a Verma object of infinite length in O c,ν . The latter result is an example of a degeneration phenomenon which can occur in rational values of ν, as was conjectured by P. Etingof.
- Subjects
ABELIAN categories; VERMA modules; FINITE groups; LIE superalgebras; INTERPOLATION
- Publication
Representation Theory, 2014, Vol 18, Issue 12, p361
- ISSN
1088-4165
- Publication type
Article
- DOI
10.1090/S1088-4165-2014-00459-X