A dynamical system connected with the inhomogeneous six-vertex model. II. Evolution of orthogonal and symplectic matrices: An algebraic-geometric description

The present paper continues part I (Zap. Nauchn. Semin. POMI, 215, 178–196 (1994)), in which a dynamical system in discrete time generazed by a birational transformation acting on the equivalence classes of matrices of specific form is introduced. We study reductions of this system on orthogonal and symmetric matrices by means of algebraic geometry. Bibliography: 4 titles.