A Fock model and the Segal-Bargmann transform for the minimal representation of the orthosymplectic Lie superalgebra osp(m,2|2n)

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 osp(m, 2\2n). We also construct an integral transform which intertwines the Schrodinger model for the minimal representation of the orthosymplectic Lie superalgebra osp (m, 2\2n) with this new Fock model.

Publication year:2020

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