Applying projective functors to arbitrary holonomic simple modules
Representation Theory
2024-01-29 v2
Abstract
We prove that applying a projective functor to a holonomic simple module over a semi-simple finite dimensional complex Lie algebra produces a module that has an essential semi-simple 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.
Cite
@article{arxiv.2311.04191,
title = {Applying projective functors to arbitrary holonomic simple modules},
author = {Marco Mackaay and Volodymyr Mazorchuk and Vanessa Miemietz},
journal= {arXiv preprint arXiv:2311.04191},
year = {2024}
}
Comments
v2: significant changes compared to v1, the main result is restricted to the case of holonomic modules