Finite-dimensional representations of the quantum superalgebraU q[gl(n/m)] and relatedq-identities

1993/06/28 by T. D. Palev, N. I. Stoilova, J. Van der Jeugt · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Artificial intelligence #Basis (linear algebra) #Class (philosophy) #Computer science #Current algebra #Geometry #Irreducible representation #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum mechanics #Set (abstract data type) #Superalgebra #Supermatrix #hep-th #math.QA

paper · pdf · doi:10.1007/bf02112320

published as Commun.Math.Phys. 166 (1994) 367-378 · 12 pages

arxiv created 1993/06/28 · openalex publication_date 1994/12/01 · arxiv updated 2009/11/30 · openalex created_date 2021/02/01 · openalex updated_date 2026/08/05

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.

Citations

• Yang-Baxter Equation in Integrable Systems
• Lie superalgebras

Cited by

• Bimodule structure of the mixed tensor product over Uqsℓ(2|1) and quantum walled Brauer algebra
• Highest weight irreducible representations of the Lie superalgebra gl(1|∞)