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arXiv · 2002.12836

A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra $\mathfrak{osp}(m,2|2n)$

Sigiswald Barbier·Sam Claerebout·Hendrik De Bie
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Abstract

The minimal representation of a semisimple Lie group is a 'small' infinite-dimensional irreducible unitary representation. It is thought to correspond to the minimal nilpotent coadjoint orbit in Kirillov's orbit philosophy. The Segal-Bargmann transform is an intertwining integral transformation between two different models of the minimal representation for Hermitian Lie groups of tube type. In this paper we construct a Fock model for the minimal representation of the orthosymplectic Lie superalgebra $\mathfrak{osp}(m,2|2n)$. We also construct an integral transform which intertwines the Schr\"odinger model for the minimal representation of the orthosymplectic Lie superalgebra $\mathfrak{osp}(m,2|2n)$ with this new Fock model.

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BibTeXRIS

Sigiswald Barbier, Sam Claerebout, Hendrik De Bie. 2020-02-28. A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra $\mathfrak{osp}(m,2|2n)$. https://doi.org/10.3842/sigma.2020.085

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