Invariants and reduced Wigner coefficients for quasi-triangular Hopf superalgebras

TL;DR

This paper derives explicit formulas for invariants and reduced Wigner coefficients in quantum supergroups, enhancing the understanding of their representation theory using characteristic identities.

Contribution

It introduces new methods to compute eigenvalues of invariants and matrix elements for $U_q[gl(m|n)]$, advancing quantum supergroup analysis.

Findings

Explicit eigenvalue formulas for invariants

Evaluation techniques for generator matrix elements

Calculation of reduced Wigner coefficients

Abstract

We develop explicit formulae for the eigenvalues of various invariants for highest weight irreducible representations of the quantum supergroup $U_q[gl(m|n)]$. The techniques employed make use of modified characteristic identity methods and allow for the evaluation of generator matrix elements and reduced Wigner coefficients.