Alldridge, Alexander ORCID: 0000-0001-6331-1672, Hilgert, Joachim and Wurzbacher, Tilmann (2018). SUPERORBITS. J. Inst. Math. Jussieu, 17 (5). S. 1065 - 1121. CAMBRIDGE: CAMBRIDGE UNIV PRESS. ISSN 1475-3030

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Abstract

We study actions of Lie supergroups, in particular, the hitherto elusive notion of orbits through odd (or more general) points. Following categorical principles, we derive a conceptual framework for their treatment and therein prove general existence theorems for the isotropy (or stabiliser) supergroups and orbits through general points. In this setting, we show that the coadjoint orbits always admit a (relative) supersymplectic structure of Kirillov-Kostant-Souriau type. Applying a family version of Kirillov's orbit method, we decompose the regular representation of an odd Abelian supergroup into an odd direct integral of characters and construct universal families of representations, parametrised by a supermanifold, for two different super variants of the Heisenberg group.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Alldridge, AlexanderUNSPECIFIEDorcid.org/0000-0001-6331-1672UNSPECIFIED
Hilgert, JoachimUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Wurzbacher, TilmannUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-168696
DOI: 10.1017/S147474801600030X
Journal or Publication Title: J. Inst. Math. Jussieu
Volume: 17
Number: 5
Page Range: S. 1065 - 1121
Date: 2018
Publisher: CAMBRIDGE UNIV PRESS
Place of Publication: CAMBRIDGE
ISSN: 1475-3030
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
UNITARY REPRESENTATIONS; SUPER; SUPERGROUPS; ORBITSMultiple languages
MathematicsMultiple languages
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/16869

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