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...

Full description

Bibliographic Details
Main Authors: Ta Khongsap, Weiqiang Wang
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2009-01-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
spin Hecke algebras
Hecke-Clifford algebras
Dunkl operators
Online Access:http://dx.doi.org/10.3842/SIGMA.2009.012
id doaj-bb0a811e8fd14452b1b3ff40416d7ed2
record_format Article
spelling doaj-bb0a811e8fd14452b1b3ff40416d7ed22020-11-24T23:57:30ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592009-01-015012Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine TypeTa KhongsapWeiqiang WangWe 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. http://dx.doi.org/10.3842/SIGMA.2009.012spin Hecke algebrasHecke-Clifford algebrasDunkl operators
collection DOAJ
language English
format Article
sources DOAJ
author Ta Khongsap
Weiqiang Wang
spellingShingle Ta Khongsap
Weiqiang Wang
Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
Symmetry, Integrability and Geometry: Methods and Applications
spin Hecke algebras
Hecke-Clifford algebras
Dunkl operators
author_facet Ta Khongsap
Weiqiang Wang
author_sort Ta Khongsap
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 National Academy of Science of Ukraine
series Symmetry, Integrability and Geometry: Methods and Applications
issn 1815-0659
publishDate 2009-01-01
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.
topic spin Hecke algebras
Hecke-Clifford algebras
Dunkl operators
url http://dx.doi.org/10.3842/SIGMA.2009.012
work_keys_str_mv AT takhongsap heckecliffordalgebrasandspinheckealgebrasivodddoubleaffinetype
AT weiqiangwang heckecliffordalgebrasandspinheckealgebrasivodddoubleaffinetype
_version_ 1725453658774044672

Similar Items