Dirac Operators for the Dunkl Angular Momentum Algebra
We define a family of Dirac operators for the Dunkl angular momentum algebra depending on certain central elements of the group algebra of the Pin cover of the Weyl group inherent to the rational Cherednik algebra. We prove an analogue of Vogan's conjecture for this family of operators and use...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2022 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211628 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Dirac Operators for the Dunkl Angular Momentum Algebra. Kieran Calvert and Marcelo De Martino. SIGMA 18 (2022), 040, 18 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862611259432632320 |
|---|---|
| author | Calvert, Kieran De Martino, Marcelo |
| author_facet | Calvert, Kieran De Martino, Marcelo |
| citation_txt | Dirac Operators for the Dunkl Angular Momentum Algebra. Kieran Calvert and Marcelo De Martino. SIGMA 18 (2022), 040, 18 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We define a family of Dirac operators for the Dunkl angular momentum algebra depending on certain central elements of the group algebra of the Pin cover of the Weyl group inherent to the rational Cherednik algebra. We prove an analogue of Vogan's conjecture for this family of operators and use this to show that the Dirac cohomology, when non-zero, determines the central character of representations of the angular momentum algebra. Furthermore, interpreting this algebra in the framework of (deformed) Howe dualities, we show that the natural Dirac element we define yields, up to scalars, a square root of the angular part of the Calogero-Moser Hamiltonian.
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| first_indexed | 2026-03-14T06:49:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211628 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T06:49:40Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Calvert, Kieran De Martino, Marcelo 2026-01-07T13:41:04Z 2022 Dirac Operators for the Dunkl Angular Momentum Algebra. Kieran Calvert and Marcelo De Martino. SIGMA 18 (2022), 040, 18 pages 1815-0659 2020 Mathematics Subject Classification: 16S37; 17B99; 20F55; 81R12 arXiv:2110.01353 https://nasplib.isofts.kiev.ua/handle/123456789/211628 https://doi.org/10.3842/SIGMA.2022.040 We define a family of Dirac operators for the Dunkl angular momentum algebra depending on certain central elements of the group algebra of the Pin cover of the Weyl group inherent to the rational Cherednik algebra. We prove an analogue of Vogan's conjecture for this family of operators and use this to show that the Dirac cohomology, when non-zero, determines the central character of representations of the angular momentum algebra. Furthermore, interpreting this algebra in the framework of (deformed) Howe dualities, we show that the natural Dirac element we define yields, up to scalars, a square root of the angular part of the Calogero-Moser Hamiltonian. This research was supported by the Heilbronn Institute for Mathematical Research and the special research fund (BOF) from Ghent University [BOF20/PDO/058]. We would also like to thank Roy Oste for the many discussions while preparing this manuscript and the anonymous referees for their comments and corrections, which greatly improved the manuscript. In particular, we would like to thank them for inspiring us to add Proposition 6.8, which guarantees that the theory of Dirac operators for the AMA is not vacuous. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dirac Operators for the Dunkl Angular Momentum Algebra Article published earlier |
| spellingShingle | Dirac Operators for the Dunkl Angular Momentum Algebra Calvert, Kieran De Martino, Marcelo |
| title | Dirac Operators for the Dunkl Angular Momentum Algebra |
| title_full | Dirac Operators for the Dunkl Angular Momentum Algebra |
| title_fullStr | Dirac Operators for the Dunkl Angular Momentum Algebra |
| title_full_unstemmed | Dirac Operators for the Dunkl Angular Momentum Algebra |
| title_short | Dirac Operators for the Dunkl Angular Momentum Algebra |
| title_sort | dirac operators for the dunkl angular momentum algebra |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211628 |
| work_keys_str_mv | AT calvertkieran diracoperatorsforthedunklangularmomentumalgebra AT demartinomarcelo diracoperatorsforthedunklangularmomentumalgebra |