Universität zu Köln

Alldridge, Alexander ORCID: 0000-0001-6331-1672 and Schmittner, Sebastian ORCID: 0000-0001-5739-4715 (2015). Spherical representations of Lie supergroups. J. Funct. Anal., 268 (6). S. 1403 - 1454. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1096-0783

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Abstract

The classical Cartan Helgason Theorem characterises finite-dimensional spherical representations of reductive Lie groups in terms of their highest weights. We generalise the theorem to the case of a reductive symmetric supergroup pair (G, K) of even type. Along the way, we compute the Harish-Chandra c-function of the symmetric superspace G/K. By way of an application, we show that in type AIII vertical bar AIII, all spherical representations are self-dual. (C) 2014 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Alldridge, Alexander UNSPECIFIED orcid.org/0000-0001-6331-1672 UNSPECIFIED Schmittner, Sebastian UNSPECIFIED orcid.org/0000-0001-5739-4715 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-404939
DOI:	10.1016/j.jfa.2014.11.018
Journal or Publication Title:	J. Funct. Anal.
Volume:	268
Number:	6
Page Range:	S. 1403 - 1454
Date:	2015
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Place of Publication:	SAN DIEGO
ISSN:	1096-0783
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language REDUCTIVE SYMMETRIC SUPERPAIRS; CARTAN-HELGASON THEOREM; BEREZIN INTEGRATION; SUPERMANIFOLDS; SPACES; CLASSIFICATION; SUPERSPACES Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/40493