A minimal representation of the orthosymplectic Lie supergroup

Sigiswald Barbier, Jan Frahm*

*Corresponding author for this work

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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.

Original languageEnglish
JournalInternational Mathematics Research Notices
Volume2021
Issue21
Pages (from-to)16357-16420
Number of pages63
ISSN1073-7928
DOIs
Publication statusPublished - 1 Nov 2021

Keywords

  • math.RT
  • 17B10, 17B60, 22E46, 58C50

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