Two-sided BGG resolutions of admissible representations

DOI10.1090/S1088-4165-2014-00454-0zbMath1367.17019arXiv1207.4276MaRDI QIDQ2922914

Tomoyuki Arakawa

Publication date: 15 October 2014

Published in: Representation Theory of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.4276

zbMATH Keywords

admissible representationparabolic subalgebraaffine Kac-Moody algebraBGG resolutionBorel-Weil theorem

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

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Weight representations of admissible affine vertex algebras ⋮ Screening operators and parabolic inductions for affine \(\mathcal{W}\)-algebras ⋮ Equivariant \(K\)-theory of semi-infinite flag manifolds and the Pieri-Chevalley formula ⋮ Realizations of simple affine vertex algebras and their modules: the cases \({\widehat{sl(2)}}\) and \({\widehat{osp(1,2)}}\) ⋮ Rationality of \(W\)-algebras: principal nilpotent cases ⋮ Rationality of admissible affine vertex algebras in the category \(\mathcal O\) ⋮ Quantum Langlands duality of representations of -algebras ⋮ \(W\)-algebras as coset vertex algebras ⋮ Tableau models for semi-infinite Bruhat order and level-zero representations of quantum affine algebras ⋮ Urod algebras and Translation of W-algebras ⋮ Higher rank partial and false theta functions and representation theory

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