Solutions of Discretized Affine Toda Field Equations for A n (1), B n (1), C n (1), D n (1), A n (2) and D n+1 (2)

It is known that a family oftransfer matrix functional equations, the T-system, can be compactly written in terms of the Cartan matrix ofa simple Lie algebra.We formally replace this Cartan matrix of a simple Lie algebra with that of an affine Lie algebra, and then we obtain a system of functional equations different from the T-system.It may be viewed as an X_n^(a) type affine Toda field equation on discrete space time. We present, for A_n⁽¹⁾, B_n⁽¹⁾, C_n⁽¹⁾, D_n⁽¹⁾, A_n⁽²⁾ and D_n+1⁽²⁾,its solutions in terms of determinants or Pfaffians.