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Gauss--Berezin integral operators, spinors over orthosymplectic supergroups, and Lagrangian super-Grassmannians
2024-12-06

We obtain explicit formulas for the spinor representation $\rho$ of the real orthosymplectic supergroup $\OSp(2p|2q,\R)$ by integral 'Gauss--Berezin' operators. Next, we extend $\rho$ to a complex domain and get a representation of a larger semigroup, which is a counterpart of Olshanski subsemigroups in semisimple Lie groups. Further, we show that $\rho$ can be extended to an operator-valued function on a certain domain in the Lagrangian super-Grassmannian (graphs of elements of the supergroup $\OSp(2p|2q,\C)$ are Lagrangian super-subspaces) and show that this function is a 'representation' in the following sense: we consider Lagrangian subspaces as linear relations and composition of two Lagrangian relations in general position corresponds to a product of Gauss--Berezin operators

Ссылка для цитирования:

Неретин Ю. А. 2024. Gauss--Berezin integral operators, spinors over orthosymplectic supergroups, and Lagrangian super-Grassmannians. PREPRINTS.RU. https://doi.org/10.24108/preprints-3113252

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