Two-sided BGG resolutions of admissible representations

Arakawa, Tomoyuki

doi:10.1090/S1088-4165-2014-00454-0

Two-sided BGG resolutions of admissible representations
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by Tomoyuki Arakawa

Represent. Theory 18 (2014), 183-222

DOI: https://doi.org/10.1090/S1088-4165-2014-00454-0

Published electronically: August 7, 2014

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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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