1998/04/01 by Zengo Tsuboi · 5 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #cond-mat.stat-mech #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/s0378-4371(97)00625-0
published as Physica A 252 (1998) 565-585 · 22 pages; some more updated information can be found in a recent paper: Nucl.Phys. B826 [PM] (2010) 399-455 (arXiv:0906.2039 [math-ph]); v2: title corrected; v3: a reference added
openalex publication_date 1998/04/01 · arxiv created 2009/12/12 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Lie superalgebra sl(r+1|s+1) admits several inequivalent choices of simple root systems. We have carried out analytic Bethe ansatz for any simple root systems of sl(r+1|s+1). We present transfer matrix eigenvalue formulae in dressed vacuum form, which are expressed as the Young supertableaux with some semistandard-like conditions. These formulae have determinant expressions, which can be viewed as quantum analogue of Jacobi-Trudi and Giambelli formulae for sl(r+1|s+1). We also propose a class of transfer matrix functional relations, which is specialization of Hirota bilinear difference equation. Using the particle-hole transformation, relations among the Bethe ansatz equations for various kinds of simple root systems are discussed.