Iwahori-Hecke type algebras associated with the Lie superalgebras A(m,n), B(m,n), C(n) and D(m,n)

TL;DR

This paper introduces Iwahori-Hecke type algebras linked to specific Lie superalgebras and classifies their irreducible representations for generic parameters.

Contribution

It constructs new algebraic structures associated with Lie superalgebras and provides a classification of their irreducible representations.

Findings

Defined Iwahori-Hecke type algebras for g=A(m,n), B(m,n), C(n), D(m,n)

Classified irreducible representations for generic q

Established foundational properties of these algebras

Abstract

In this paper we give Iwahori-Hecke type algebras H_q(g) associated with the Lie superalgebras g=A(m,n), B(m,n), C(n) and D(m,n). We classify the irreducible representations of H_q(g) for generic q.