 Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1∣s+1)Zengo Tsuboi Physica A: Statistical Mechanics and its Applications, 1998, vol. 252, issue 3, 565-585 Abstract: 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. Keywords: Analytic Bethe ansatz; Lie superalgebra; Solvable lattice model; Transfer matrix; T-system; Young superdiagram (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:252:y:1998:i:3:p:565-585 DOI: 10.1016/S0378-4371(97)00625-0 Access Statistics for this article Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis More articles in Physica A: Statistical Mechanics and its Applications from Elsevier |
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