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Cohomology in singular blocks of parabolic category $\mathcal{O}$

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  15 May 2023

Jonathan Gruber Open the ORCID record for Jonathan Gruber [Opens in a new window]
Jonathan Gruber*
Affiliation:
Department of Mathematics, National University of Singapore, Singapore, Singapore
*
E-mail: jgruber@nus.edu.sg
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Abstract

We determine the dimensions of $\textrm{Ext}$-groups between simple modules and dual generalized Verma modules in singular blocks of parabolic versions of category $\mathcal{O}$ for complex semisimple Lie algebras and affine Kac-Moody algebras.

Keywords

cohomologyLie algebraKac-Moody algebraKoszul duality

MSC classification

Primary: 17B55: Homological methods in Lie (super)algebras 17B10: Representations, algebraic theory (weights)
Secondary: 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 65 , Issue 3 , September 2023 , pp. 555 - 568
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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