Two-sided BGG resolutions of admissible representations

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-infintie analogue of the generalized Borel-Weil theorem for mimimal parabolic subalgebras which enables an inductive study of admissible representations.

revised, to appear in Representation Theory

References in corpus (1)

• Rationality of admissible affine vertex algebras in the category O

Cited by in corpus (11)

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• Rationality of W-algebras: principal nilpotent cases
• Rationality of admissible affine vertex algebras in the category O
• Trialities of $\mathcal{W}$-algebras
• Weight representations of admissible affine vertex algebras
• Quantum Langlands duality of representations of W-algebras
• Equivariant $K$-theory of semi-infinite flag manifolds and Pieri-Chevalley formula
• Screening operators and Parabolic inductions for Affine W-algebras (with an appendix by Shigenori Nakatsuka)
• Realizations of simple affine vertex algebras and their modules: the cases $\widehat{sl(2)}$ and $\widehat{osp(1,2)}$
• Orthosymplectic Feigin-Semikhatov duality
• Connecting affine $\mathcal{W}$-algebras: A case study on ${\mathfrak{sl}}_4$