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.

arXiv comment43 pages

References in corpus (14)

• The N=4 SYM Integrable Super Spin Chain
• The GL(1|1) WZW model: From Supergeometry to Logarithmic CFT
• Continuum Limit of the Integrable sl(2/1) 3-\bar{3} Superspin Chain
• Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-Mills
• R-matrices and Spectrum of Vertex Models based on Superalgebras
• Analytical Bethe Ansatz for closed and open gl(M|N) super-spin chains in arbitrary representations and for any Dynkin diagram
• 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
• Determinant Representations of Correlation Functions for the Supersymmetric t-J Model
• Gel'fand-Zetlin Basis and Clebsch-Gordan Coefficients for Covariant Representations of the Lie superalgebra gl(m|n)
• A class of quadratic deformations of Lie superalgebras
• Wigner-Eckart theorem for tensor operators of Hopf algebras
• Tensor operators and Wigner-Eckart theorem for the quantum superalgebra U_{q}[osp(1\mid 2)]

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