Hecke-Clifford algebras and spin Hecke algebras I: the classical affine type

TL;DR

This paper introduces new algebraic structures called degenerate spin affine Hecke algebras and affine Hecke-Clifford algebras related to classical Weyl groups, establishing foundational properties and connections with existing affine Hecke algebras.

Contribution

It defines these new algebras, proves their PBW properties, describes their centers, and links them to Lusztig's degenerate affine Hecke algebras through covering algebras.

Findings

Established PBW properties for the new algebras

Described the centers of these algebras

Connected these algebras to Lusztig's degenerate affine Hecke algebras

Abstract

Associated to the classical Weyl groups, we introduce the notion of degenerate spin affine Hecke algebras and affine Hecke-Clifford algebras. For these algebras, we establish the PBW properties, formulate the intertwiners, and describe the centers. We further develop connections of these algebras with the usual degenerate (i.e. graded) affine Hecke algebras of Lusztig by introducing a notion of degenerate covering affine Hecke algebras.