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

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