Supersymmetric Bethe ansatz and Baxter equations from discrete Hirota dynamics

We show that eigenvalues of the family of Baxter Q  -operators for supersymmetric integrable spin chains constructed with the gl(K|M)gl(K|M)-invariant R-matrix obey the Hirota bilinear difference equation. The nested Bethe ansatz for super-spin chains, with any choice of simple root system, is then treated as a discrete dynamical system for zeros of polynomial solutions to the Hirota equation. Our basic tool is a chain of Bäcklund transformations for the Hirota equation connecting quantum transfer matrices. This approach also provides a systematic way to derive the complete set of generalized Baxter equations for super-spin chains.