Fr\'echet globalisations of Harish-Chandra supermodules
Representation Theory
2017-10-05 v2 Mathematical Physics
math.MP
Abstract
For any Lie supergroup whose underlying Lie group is reductive, we prove an extension of the Casselman-Wallach globalisation theorem: There is an equivalence between the category of Harish-Chandra modules and the category of SF-representations (smooth Fr\'echet representations of moderate growth) whose module of finite vectors is Harish-Chandra. As an application, we extend to Lie supergroups a general general form of the Gel'fand-Kazhdan criterion due to Sun-Zhu.
Cite
@article{arxiv.1403.4055,
title = {Fr\'echet globalisations of Harish-Chandra supermodules},
author = {Alexander Alldridge},
journal= {arXiv preprint arXiv:1403.4055},
year = {2017}
}
Comments
33 pages; final version accepted for publication in Int. Math. Res. Not. IMRN