Analytic Bethe ansatz related to a one-parameter family of finite-dimensional representations of the Lie superalgebra

1998/06/19 by Zengo Tsuboi · 4 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #cond-mat.stat-mech #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/0305-4470/31/24/010

published as J. Phys. A: Math. Gen. 31 (1998) 5485-5498 · 19 pages; some more updated information can be found in a recent paper: Nucl.Phys. B826 [PM] (2010) 399-455 (arXiv:0906.2039 [math-ph])

openalex publication_date 1998/06/19 · arxiv created 2009/11/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

As is well known, the type 1 Lie superalgebra admits a one-parameter family of finite-dimensional irreducible representations. We have carried out an analytic Bethe ansatz related to this family of representations. We present formulae, which are deformations of previously proposed determinant formulae labelled by a Young superdiagram. These formulae will provide a transfer matrix eigenvalue in a dressed vacuum form related to the solutions of a graded Yang-Baxter equation, which depend not only on the spectral parameter but also on a non-additive continuous parameter. A class of transfer matrix functional relations among these formulae is briefly mentioned.

Citations

• Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1∣s+1)
• Quantum affine algebras and deformations of the Virasoro and 237-1237-1237-1
• The gl (M|N) super Yangian and its finite-dimensional representations
• Analytic Bethe ansatz and functional equations for Lie superalgebra

Cited by

• Analytic Bethe ansatz and functional relations related to tensor-like representations of type-II Lie superalgebrasB(r|s) andD(r|s)
• Analytic Bethe ansatz related to the Lie superalgebra C(s)
• The nested Bethe ansatz for ‘all’ closed spin chains
• Noncompact sl(N) Spin Chains: BGG-Resolution, Q-Operators and Alternating Sum Representation for Finite-Dimensional Transfer Matrices