Invariants and reduced matrix elements associated with the Lie superalgebra gl(m|n)

TL;DR

This paper develops explicit formulas for eigenvalues of invariants in the Lie superalgebra gl(m|n), linking them to reduced matrix elements and Wigner coefficients, advancing algebraic methods for matrix element calculations.

Contribution

It introduces explicit eigenvalue formulas for invariants of gl(m|n) and connects them to reduced matrix elements, enabling algebraic derivations of generator matrix elements.

Findings

Explicit eigenvalue formulas for invariants of gl(m|n)

Connection between eigenvalues and reduced Wigner coefficients

Foundation for algebraic derivation of matrix elements

Abstract

We construct explicit formulae for the eigenvalues of certain invariants of the Lie superalgebra gl(m|n) using characteristic identities. We discuss how such eigenvalues are related to reduced Wigner coefficients and the reduced matrix elements of generators, and thus provide a first step to a new algebraic derivation of matrix element formulae for all generators of the algebra.