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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On representations of rational Cherednik algebras of complex rank
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by Inna Entova Aizenbud
Represent. Theory 18 (2014), 361-407
Published electronically: November 24, 2014


We study a family of abelian categories $\underline {\mathcal {O}}_{\text { } c,\nu }$ depending on complex parameters $c, \nu$ which are interpolations of the category $\mathcal {O}$ for the rational Cherednik algebra $H_c(\nu )$ of type $A$, where $\nu$ 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 $c, \nu$, and prove that a Verma object of infinite length exists in $\mathcal {O}_{\text { } c,\nu }$ only if $c \in \mathbb {Q}_{<0}$. We also show that for every $c \in \mathbb {Q}_{<0}$ there exists $\nu \in \mathbb {Q}_{<0}$ such that there exists a Verma object of infinite length in $\mathcal {O}_{\text { } c,\nu }$.

The latter result is an example of a degeneration phenomenon which can occur in rational values of $\nu$, as was conjectured by P. Etingof.

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Bibliographic Information
  • Inna Entova Aizenbud
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • Email:
  • Received by editor(s): March 17, 2014
  • Received by editor(s) in revised form: June 14, 2014, and September 17, 2014
  • Published electronically: November 24, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: Represent. Theory 18 (2014), 361-407
  • MSC (2010): Primary 16S99, and, 18D10
  • DOI:
  • MathSciNet review: 3280664