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

Published 2020-02-28Version 1

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.