A Schr\"odinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra $D(2,1;\alpha)$

Sigiswald Barbier; Sam Claerebout

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arXiv · 2104.00326

A Schr\"odinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra $D(2,1;\alpha)$

Sigiswald Barbier·Sam Claerebout

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Abstract

We construct two infinite-dimensional irreducible representations for $D(2,1;\alpha)$: a Schr\"odinger model and a Fock model. Further, we also introduce an intertwining isomorphism. These representations are similar to the minimal representations constructed for the orthosymplectic Lie supergroup and for Hermitian Lie groups of tube type. The intertwining isomorphism is the analogue of the Segal-Bargmann transform for the orthosymplectic Lie supergroup and for Hermitian Lie groups of tube type.

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BibTeX RIS

Sigiswald Barbier, Sam Claerebout. 2021-04-01. A Schr\"odinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra $D(2,1;\alpha)$. https://arxiv.org/abs/2104.00326

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