Analytic Bethe ansatz related to a one-parameter family of finite-dimensional representations of the Lie superalgebra

As is well known, the type 1 Lie superalgebra admits a one-parameter family of finite-dimensional irreducible representations. We have carried out an analytic Bethe ansatz related to this family of representations. We present formulae, which are deformations of previously proposed determinant formulae labelled by a Young superdiagram. These formulae will provide a transfer matrix eigenvalue in a dressed vacuum form related to the solutions of a graded Yang-Baxter equation, which depend not only on the spectral parameter but also on a non-additive continuous parameter. A class of transfer matrix functional relations among these formulae is briefly mentioned.