Applying projective functors to arbitrary holonomic simple modules

Mackaay, Marco, Mazorchuk, Volodymyr and Miemietz, Vanessa (2024) Applying projective functors to arbitrary holonomic simple modules. Journal of the London Mathematical Society-Second Series, 110 (2). ISSN 0024-6107

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Abstract

We prove that applying a projective functor to a holonomic simple module over a semisimple finite-dimensional complex Lie algebra produces a module that has an essential semisimple submodule of finite length. This implies that holonomic simple supermodules over certain Lie superalgebras are quotients of modules that are induced from simple modules over the even part. We also provide some further insight into the structure of Lie algebra modules that are obtained by applying projective functors to simple modules.

Item Type:	Article
Additional Information:	Funding information: Fundação para a Ciência e a Tecnologia. Grant Number: UID/MAT/04459/2013; Swedish Research Council
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Depositing User:	LivePure Connector
Date Deposited:	04 Jun 2024 12:30
Last Modified:	21 Dec 2024 01:09
URI:	https://ueaeprints.uea.ac.uk/id/eprint/95381
DOI:	10.1112/jlms.12965

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