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Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type

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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Main Authors: Khongsap, T., Wang, W.
Format: Article
Language:English
Published: Інститут математики НАН України 2009
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/149249
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spelling irk-123456789-1492492019-02-20T01:26:54Z Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type Khongsap, T. Wang, W. 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. 2009 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149249 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author Khongsap, T.
Wang, W.
spellingShingle Khongsap, T.
Wang, W.
Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Khongsap, T.
Wang, W.
author_sort Khongsap, T.
title 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_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
publisher Інститут математики НАН України
publishDate 2009
url http://dspace.nbuv.gov.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.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT khongsapt heckecliffordalgebrasandspinheckealgebrasivodddoubleaffinetype
AT wangw heckecliffordalgebrasandspinheckealgebrasivodddoubleaffinetype
first_indexed 2023-05-20T17:32:33Z
last_indexed 2023-05-20T17:32:33Z
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