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

Symmetry Integrability and Geometry-Methods and Applications

article

Sigiswald Barbier¹  Sam Claerebout¹  Hendrik De Bie¹ 

[1] Department of Electronics and Information Systems, Faculty of Engineering and Architecture, Ghent University

关键词: Segal–Bargmann transform;    Fock model;    Schr¨odinger model;    minimal representations;    Lie superalgebras;    spherical harmonics;    Bessel–Fischer product 2020 Mathematics Subject Classification 17B10;    17B60;    22E46;    58C50;   

DOI  :  10.3842/SIGMA.2020.085

来源: National Academy of Science of Ukraine

【 摘 要 】

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 Schrödinger model for the minimal representation of the orthosymplectic Lie superalgebra $\mathfrak{osp}(m,2|2n)$ with this new Fock model.

【 授权许可】

Unknown