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Kostant’s problem for parabolic Verma modules

Part of: Algebraic combinatorics Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  27 January 2025

Volodymyr Mazorchuk Open the ORCID record for Volodymyr Mazorchuk [Opens in a new window]  and
Shraddha Srivastava
Volodymyr Mazorchuk
Affiliation:
Department of Mathematics, Uppsala University, Uppsala, Sweden
Shraddha Srivastava*
Affiliation:
Department of Mathematics, Indian Institute of Technology, Dharwad, India
*
Corresponding author: Shraddha Srivastava, email: maths.shraddha@gmail.com
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Abstract

We give a complete combinatorial classification of the parabolic Verma modules in the principal block of the parabolic category $\mathcal{O}$ associated with a minimal or a maximal parabolic subalgebra of the special linear Lie algebra for which the answer to Kostant’s problem is positive.

Keywords

parabolic Verma modulesKostant’s problemHecke algebrasHarish-Chandra bimodulesprojective functors

MSC classification

Primary: 17B10: Representations, algebraic theory (weights) 17B35: Universal enveloping (super)algebras
Secondary: 05E10: Combinatorial aspects of representation theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , First View , pp. 1 - 22
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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