Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1|s+1)
arXiv:0911.5387 · doi:10.1016/S0378-4371(97)00625-0
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.
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
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