Geodesic
A Schrödinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra D(2,1;α)
Sigiswald Barbier1 ; Sam Claerebout1
1Dept. of Electronics and Information Systems, Faculty of Engineering and Architecture, Ghent University, Belgium
Journal of Lie Theory, Tome 31 (2021) no. 4, pp. 1153-1188

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 17B10, 17B60, 22E46, 58C50
Mots-clés : Fock model, Schrödinger model, minimal representations, Lie superalgebras, Bessel-Fischer product, Segal-Bargmann transform

Sigiswald Barbier  1   ; Sam Claerebout  1

1 Dept. of Electronics and Information Systems, Faculty of Engineering and Architecture, Ghent University, Belgium 
Sigiswald Barbier; Sam Claerebout. A Schrödinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra D(2,1;α). Journal of Lie Theory, Tome 31 (2021) no. 4, pp. 1153-1188. http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a16/
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     author = {Sigiswald Barbier and Sam 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},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a16/}
}
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