A minimal representation of the orthosymplectic Lie supergroup

Sigiswald Barbier, Jan Frahm*

*Corresponding author af dette arbejde

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Abstract

We construct a minimal representation of the orthosymplectic Lie supergroup OSp(p, q|2n) for p + q even, generalizing the Schr dinger model of the minimal representation of O(p, q) to the super case. The underlying Lie algebra representation is realized on functions on the minimal orbit inside the Jordan superalgebra associated with osp(p, q|2n), so that our construction is in line with the orbit philosophy. Its annihilator is given by a Joseph-like ideal for osp(p, q|2n), and therefore the representation is a natural generalization of a minimal representation to the context of Lie superalgebras. We also calculate its Gelfand Kirillov dimension and construct a nondegenerate sesquilinear form for which the representation is skew-symmetric and which is the analogue of an L2-inner product in the supercase.

OriginalsprogEngelsk
TidsskriftInternational Mathematics Research Notices
Vol/bind2021
Nummer21
Sider (fra-til)16357-16420
Antal sider63
ISSN1073-7928
DOI
StatusUdgivet - 1 nov. 2021

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