Journal of Lie Theory

no. 4
A Schrödinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra D(2,1;α)
Journal of Lie Theory, Volume 31 (2021) no. 4, pp. 1153-1188
We construct two infinite-dimensional irreducible representations for D(2,1;α): a Schrödinger 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.
DOI: 10.5802/jolt.1216
Classification: 17B10, 17B60, 22E46, 58C50
Keywords: Fock model, Schrödinger model, minimal representations, Lie superalgebras, Bessel-Fischer product, Segal-Bargmann transform 
@article{JOLT_2021_31_4_a16,
     author = {S. Barbier and S. Claerebout},
     title = {A {Schr\"odinger} model, {Fock} model and intertwining {Segal-Bargmann} transform for the exceptional {Lie} superalgebra {D(2,1;\ensuremath{\alpha})}},
     journal = {Journal of Lie Theory},
     pages = {1153--1188},
     year = {2021},
     volume = {31},
     number = {4},
     doi = {10.5802/jolt.1216},
     zbl = {1484.17013},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1216/}
}
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%A S. Claerebout
%T A Schrödinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra D(2,1;α)
%J Journal of Lie Theory
%D 2021
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S. Barbier; S. Claerebout. A Schrödinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra D(2,1;α). Journal of Lie Theory, Volume 31 (2021) no. 4, pp. 1153-1188. doi: 10.5802/jolt.1216

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