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arXiv · 0911.5387

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

Zengo Tsuboi
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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.

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Zengo Tsuboi. 2009-12-12. Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1|s+1). https://doi.org/10.1016/s0378-4371(97)00625-0

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