A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra (, 2|2)
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 tran...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2020 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2020
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210763 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra (, 2|2). Sigiswald Barbier, Sam Claerebout and Hendrik De Bie. SIGMA 16 (2020), 085, 33 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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 (, 2|2). We also construct an integral transform which intertwines the Schrödinger model for the minimal representation of the orthosymplectic Lie superalgebra (, 2|2) with this new Fock model.
|
|---|---|
| ISSN: | 1815-0659 |