Frobenius nil-Hecke algebras

Alistair Savage and John Stuart

Vol. 311 (2021), No. 2, 455–473

DOI: 10.2140/pjm.2021.311.455

Abstract

To any Frobenius superalgebra $A$ we associate towers of Frobenius nil-Coxeter algebras and Frobenius nil-Hecke algebras. These act naturally, via Frobenius divided difference operators, on Frobenius polynomial algebras. When $A$ is the ground ring, our algebras recover the classical nil-Coxeter and nil-Hecke algebras. When $A$ is the two-dimensional Clifford algebra, they are Morita equivalent to the odd nil-Coxeter and odd nil-Hecke algebras.

Keywords

nilCoxeter algebra, nilHecke algebra, Frobenius algebra, divided difference operator, Demazure operator

Mathematical Subject Classification

Primary: 20C08

Milestones

Received: 25 August 2020

Accepted: 27 January 2021

Published: 31 July 2021