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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2009 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149249 |
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| Cite this: | 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. |
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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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type |
| spellingShingle |
Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type Khongsap, T. Wang, W. |
| title_short |
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_sort |
hecke-clifford algebras and spin hecke algebras iv: odd double affine type |
| author |
Khongsap, T. Wang, W. |
| author_facet |
Khongsap, T. Wang, W. |
| publishDate |
2009 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149249 |
| 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. |
| work_keys_str_mv |
AT khongsapt heckecliffordalgebrasandspinheckealgebrasivodddoubleaffinetype AT wangw heckecliffordalgebrasandspinheckealgebrasivodddoubleaffinetype |
| first_indexed |
2025-12-07T17:57:07Z |
| last_indexed |
2025-12-07T17:57:07Z |
| _version_ |
1850873193158410240 |