On (super)symmetrizing forms and Schur elements of cyclotomic Hecke-Clifford algebras

Paper

Abstract

In this paper, we introduce Schur elements for supersymmetrizing superalgebras. We show that the cyclotomic Hecke-Clifford algebra

is supersymmetric if

and, symmetric if

and an invertibility condition holds. In the semisimple case, we compute the Schur elements for both

and the cyclotomic Sergeev algebra

. As applications, we define new symmetrizing forms on the Hecke-Clifford algebra

and on the cyclotomic quiver Hecke algebras of types

and