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Two-sided BGG resolutions of admissible representations


Author: Tomoyuki Arakawa
Journal: Represent. Theory 18 (2014), 183-222
MSC (2010): Primary 06B15, 17B67, 81R10
DOI: https://doi.org/10.1090/S1088-4165-2014-00454-0
Published electronically: August 7, 2014
MathSciNet review: 3244449
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Abstract: 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
Email: arakawa@kurims.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/S1088-4165-2014-00454-0
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.
Article copyright: © Copyright 2014 American Mathematical Society

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