Hecke-Clifford algebras and spin Hecke algebras II: the rational double affine type

Details Hecke-Clifford algebras and spin Hecke algebras II: the rational double affine type Hecke-Clifford algebras and spin Hecke algebras II: the rational double affine type

2007-10-31

arxiv.org/abs/0710.5877v3

Pacific J. Math. 238 (2008), 73--103.

Mathematics

Representation Theory

v3, 32 pages, mild corrections of some typos, to appear in Pacific J. Math

Scientific paper

The notion of rational spin double affine Hecke algebras (sDaHa) and rational double affine Hecke-Clifford algebras (DaHCa) associated to classical Weyl groups are introduced. The basic properties of these algebras such as the PBW basis and Dunkl operator representations are established. An algebra isomorphism relating the rational DaHCa to the rational sDaHa is obtained. We further develop a link between the usual rational Cherednik algebra and the rational sDaHa by introducing a notion of rational covering double affine Hecke algebras.

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