Abstract

This paper introduces the notion of rational spin double afine Hecke algebras (sDaHa) and rational double afine 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 afine Hecke algebras.

Keywords

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

Mathematical Subject Classification

Primary: 20C08

Authors