Finite-dimensional representations of the quantum superalgebra $U_q[gl(n/m)]$ and related q-identities

TL;DR

This paper provides explicit formulas for the generators of the quantum superalgebra $U_q[gl(n/m)]$ acting on typical irreducible representations, reducing the verification of algebra relations to $q$-number identities.

Contribution

It introduces explicit generator expressions for $U_q[gl(n/m)]$ on typical irreducible representations and simplifies relation verification to $q$-number identities.

Findings

Explicit generator formulas for $U_q[gl(n/m)]$

Verification reduces to $q$-number identities

Applicable to all essentially typical representations

Abstract

Explicit expressions for the generators of the quantum superalgebra $U_q[gl(n/m)]$ acting on a class of irreducible representations are given. The class under consideration consists of all essentially typical representations: for these a Gel'fand-Zetlin basis is known. The verification of the quantum superalgebra relations to be satisfied is shown to reduce to a set of $q$-number identities.