Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1|s+1)

Details Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1|s+1) Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1|s+1)

2009-11-28

arxiv.org/abs/0911.5387v3

Physica A 252 (1998) 565-585

Physics

Mathematical Physics

22 pages; some more updated information can be found in a recent paper: Nucl.Phys. B826 [PM] (2010) 399-455 (arXiv:0906.2039 [

Scientific paper

10.1016/S0378-4371(97)00625-0

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.

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