Finite-dimensional representations of the quantum superalgebra $U_q[gl(n/m)]$ and related q-identities

Abstract

Explicit expressions for the generators of the quantum superalgebra $U_q[gl(n/m)]$ acting on a class of irreducible representations are given. The class under consideration consists of all essentially typical representations: for these a Gel'fand-Zetlin basis is known. The verification of the quantum superalgebra relations to be satisfied is shown to reduce to a set of $q$-number identities.

12 pages

References in corpus (1)

• Finite Dimensional Representations of the Quantum Superalgebra $U_q[gl(3/2)]$ in a Reduced $U_q[gl(3/2)]\supset U_q[gl(3/1)]\supset U_q[gl(3)]$ Basis

Cited by in corpus (21)

• Representations of Quantum Affine Superalgebras
• Classical and Quantum sl(1|2) Superalgebras, Casimir Operators and Quantum Chain Hamiltonians
• Gel'fand-Zetlin Basis and Clebsch-Gordan Coefficients for Covariant Representations of the Lie superalgebra gl(m|n)
• Infinitely many two-variable generalisations of the Alexander-Conway polynomial
• Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)
• Classification of the quantum deformation of the superalgebra $GL(1|1)$
• Finite-Dimensional Representations of the Quantum Superalgebra U${}_q$[gl(2/2)]: II. Nontypical representations at generic $q$
• Centre and Representations of U_q(sl(2|1)) at Roots of Unity
• Geometry and Representations of the Quantum Supergroup OSPq(1|2n)
• Asymptotic Representations of Quantum Affine Superalgebras
• Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra
• A Holstein-Primakoff and Dyson Realizations for the Lie Superalgebra gl(m/n+1)
• A description of the quantum superalgebra $U_q[sl(n+1|m)]$ via creation and annihilation generators
• Highest weight irreducible representations of the quantum algebra $U_h(A_{\infty })$
• Automatic Construction of Explicit R Matrices for the One-Parameter Families of Irreducible Typical Highest Weight (0|α) Representations of U_q[gl(m|n)]
• A Dyson realization and a Holstein-Primakoff realization for the quantum superalgebra $U_q[gl(n/m)]$
• Bimodule structure of the mixed tensor product over $U_{q}s\ell (2|1)$ and quantum walled Brauer algebra
• Jacobson generators of the quantum superalgebra $U_q[sl(n+1|m)]$ and Fock representations
• Highest weight irreducible representations of the Lie superalgebra $gl(1/\infty )$
• Irreducible highest weight representations of the quantum algebra $U_h(A_{\infty })$
• Irreducible representations of Upq[gl(2/2)]