Universität zu Köln

Alldridge, Alexander ORCID: 0000-0001-6331-1672 (2017). Frechet Globalisations of Harish-Chandra Supermodules. Int. Math. Res. Notices, 2017 (17). S. 5182 - 5233. OXFORD: OXFORD UNIV PRESS. ISSN 1687-0247

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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 Frechet representations of moderate growth) whose module of finite vectors is Harish-Chandra. As an application, we extend to Lie supergroups a general form of the Gelfand-Kazhdan criterion due to Sun-Zhu.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Alldridge, Alexander UNSPECIFIED orcid.org/0000-0001-6331-1672 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-220146
DOI:	10.1093/imrn/rnw155
Journal or Publication Title:	Int. Math. Res. Notices
Volume:	2017
Number:	17
Page Range:	S. 5182 - 5233
Date:	2017
Publisher:	OXFORD UNIV PRESS
Place of Publication:	OXFORD
ISSN:	1687-0247
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language UNITARY IRREDUCIBLE REPRESENTATIONS; LIE SUPERGROUPS; ALGEBRAS; CLASSIFICATION; EXTENSIONS; THEOREMS Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/22014