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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.

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Two-sided BGG resolutions of admissible representations
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by Tomoyuki Arakawa
Represent. Theory 18 (2014), 183-222
Published electronically: August 7, 2014


We prove the conjecture of Frenkel, Kac and Wakimoto on the existence of two-sided BGG resolutions of $G$-integrable admissible representations of affine Kac-Moody algebras at fractional levels. As an application we establish the semi-infinite analogue of the generalized Borel-Weil theorem for minimal parabolic subalgebras which enables an inductive study of admissible representations.
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Bibliographic Information
  • Tomoyuki Arakawa
  • Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502 Japan
  • MR Author ID: 611463
  • Email:
  • Received by editor(s): April 9, 2013
  • Received by editor(s) in revised form: April 10, 2013, and June 6, 2014
  • Published electronically: August 7, 2014
  • Additional Notes: This work was partially supported by JSPS KAKENHI Grant Number No. 20340007 and No. 23654006.
  • © Copyright 2014 American Mathematical Society
  • Journal: Represent. Theory 18 (2014), 183-222
  • MSC (2010): Primary 06B15, 17B67, 81R10
  • DOI:
  • MathSciNet review: 3244449