Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
We introduce an odd double affine Hecke algebra (DaHa) generated by a classical Weyl group W and two skew-polynomial subalgebras of anticommuting generators. This algebra is shown to be Morita equivalent to another new DaHa which are generated by W and two polynomial-Clifford subalgebras. There is y...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2009 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149249 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type / T. Khongsap, W. Wang // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 17 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862715315522109440 |
|---|---|
| author | Khongsap, T. Wang, W. |
| author_facet | Khongsap, T. Wang, W. |
| citation_txt | Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type / T. Khongsap, W. Wang // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 17 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We introduce an odd double affine Hecke algebra (DaHa) generated by a classical Weyl group W and two skew-polynomial subalgebras of anticommuting generators. This algebra is shown to be Morita equivalent to another new DaHa which are generated by W and two polynomial-Clifford subalgebras. There is yet a third algebra containing a spin Weyl group algebra which is Morita (super)equivalent to the above two algebras. We establish the PBW properties and construct Verma-type representations via Dunkl operators for these algebras.
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| first_indexed | 2025-12-07T17:57:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149249 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:57:07Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Khongsap, T. Wang, W. 2019-02-19T19:21:36Z 2019-02-19T19:21:36Z 2009 Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type / T. Khongsap, W. Wang // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 17 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 20C08 https://nasplib.isofts.kiev.ua/handle/123456789/149249 We introduce an odd double affine Hecke algebra (DaHa) generated by a classical Weyl group W and two skew-polynomial subalgebras of anticommuting generators. This algebra is shown to be Morita equivalent to another new DaHa which are generated by W and two polynomial-Clifford subalgebras. There is yet a third algebra containing a spin Weyl group algebra which is Morita (super)equivalent to the above two algebras. We establish the PBW properties and construct Verma-type representations via Dunkl operators for these algebras. This paper is a contribution to the Special Issue on Dunkl Operators and Related Topics. This research is partially supported by NSF grant DMS-0800280. The main results of this paper for type A were obtained at MSRI in 2006. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type Article published earlier |
| spellingShingle | Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type Khongsap, T. Wang, W. |
| title | Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type |
| title_full | Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type |
| title_fullStr | Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type |
| title_full_unstemmed | Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type |
| title_short | Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type |
| title_sort | hecke-clifford algebras and spin hecke algebras iv: odd double affine type |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149249 |
| work_keys_str_mv | AT khongsapt heckecliffordalgebrasandspinheckealgebrasivodddoubleaffinetype AT wangw heckecliffordalgebrasandspinheckealgebrasivodddoubleaffinetype |