Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)

TL;DR

This paper derives explicit matrix element formulas for all generators of type 2 unitary irreducible modules of the Lie superalgebra gl(m|n), revealing a phase relation with type 1 modules.

Contribution

It extends the characteristic identity formalism to compute matrix elements for all generators, including non-elementary ones, in type 2 unitary representations of gl(m|n).

Findings

Matrix element formulas for all generators are obtained.

Type 2 and type 1 matrix element equations coincide up to a phase.

Explicit phases for matrix elements are determined.

Abstract

The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible $gl(m|n)$ modules. In particular, we give matrix element formulae for all gl(m|n) generators, including the non-elementary generators, together with their phases on finite dimensional type 2 unitary irreducible representations. Remarkably, we find that the type 2 unitary matrix element equations coincide with the type 1 unitary matrix element equations for non-vanishing matrix elements up to a phase.