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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210763 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730199645290496 |
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| author | Barbier, Sigiswald Claerebout, Sam De Bie, Hendrik |
| author_facet | Barbier, Sigiswald Claerebout, Sam De Bie, Hendrik |
| citation_txt | 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 |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2026-04-17T14:59:09Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210763 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T14:59:09Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Barbier, Sigiswald Claerebout, Sam De Bie, Hendrik 2025-12-17T14:30:17Z 2020 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 1815-0659 2020 Mathematics Subject Classification: 17B10; 17B60; 22E46; 58C50 arXiv:2002.12836 https://nasplib.isofts.kiev.ua/handle/123456789/210763 https://doi.org/10.3842/SIGMA.2020.085 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. SB is supported by a BOF Postdoctoral Fellowship from Ghent University. HDB is supported by the Research Foundation Flanders (FWO) under Grant EOS 30889451. The authors would like to thank the anonymous referees for carefully reading the paper and for their useful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra (, 2|2) Article published earlier |
| spellingShingle | A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra (, 2|2) Barbier, Sigiswald Claerebout, Sam De Bie, Hendrik |
| title | A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra (, 2|2) |
| title_full | A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra (, 2|2) |
| title_fullStr | A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra (, 2|2) |
| title_full_unstemmed | A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra (, 2|2) |
| title_short | A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra (, 2|2) |
| title_sort | fock model and the segal-bargmann transform for the minimal representation of the orthosymplectic lie superalgebra (, 2|2) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210763 |
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