Analytic Bethe ansatz and functional equations for Lie superalgebra sl(r+1|s+1)

Abstract

From the point of view of the Young superdiagrm method, an analytic Bethe ansatz is carried out for Lie superalgebra sl(r+1|s+1). For the transfer matrix eigenvalue formulae in dressed vacuum form, we present some expressions, which are quantum analogue of Jacobi-Trudi and Giambelli formulae for Lie superalgebra sl(r+1|s+1). We also propose transfer matrix functional relations, which are Hirota bilinear difference equation with some constraints.