Hecke–Clifford algebras and spin Hecke algebras, II: The rational double affine type

Ta Khongsap and Weiqiang Wang

Vol. 238 (2008), No. 1, 73–103

DOI: 10.2140/pjm.2008.238.73

Abstract

This paper introduces the notion of rational spin double affine Hecke algebras (sDaHa) and rational double affine Hecke–Clifford algebras (DaHCa) associated to classical Weyl groups, and establishes the basic properties of these algebras, such as the PBW basis and Dunkl operator representations. We obtain an algebra isomorphism relating the rational DaHCa to the rational sDaHa. 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.

Keywords

Cherednik algebras, Hecke algebras, symplectic reflection algebras, Clifford algebras, superalgebras, projective representation theory

Mathematical Subject Classification 2000

Primary: 20C08

Milestones

Received: 14 February 2008

Revised: 6 August 2008

Accepted: 7 August 2008

Published: 1 November 2008