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

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.

43 pages

References in corpus (5)

• Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-Mills
• On the Percolation BCFT and the Crossing Probability of Watts
• The parafermion Fock space and explicit so(2n+1) representations
• Finite size properties of staggered $U_q[sl(2|1)]$ superspin chains
• A class of quadratic deformations of Lie superalgebras

Cited by in corpus (10)

• The $Z_2\times Z_2$-graded general linear Lie superalgebra
• A class of infinite-dimensional representations of the Lie superalgebra osp(2m+1|2n) and the parastatistics Fock space
• Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)
• Characteristic identities for Lie (super)algebras
• Representations of the Lie superalgebra $B(\infty ,\infty )$ and parastatistics Fock spaces
• Reduced Wigner coefficients for Lie superalgebra gl(m|n) corresponding to unitary representations and beyond
• Reduced matrix elements of the orthosymplectic Lie superalgebra
• Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)
• 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