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

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.

24 pages. arXiv admin note: text overlap with arXiv:1311.4246

References in corpus (2)

• Invariants and reduced matrix elements associated with the Lie superalgebra gl(m|n)
• Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)

Cited by in corpus (3)

• Reduced Wigner coefficients for Lie superalgebra gl(m|n) corresponding to unitary representations and beyond
• Invariants and matrix elements of the quantum group $U_q[gl(n,\mathbb{C})]$ revisited
• Invariants and reduced Wigner coefficients for quasi-triangular Hopf superalgebras