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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Two-sided BGG resolutions of admissible representations
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by Tomoyuki Arakawa PDF
Represent. Theory 18 (2014), 183-222 Request permission


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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Additional 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