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)}

Abstract

It is known that a family of transfer matrix functional equations, the T-system, can be compactly written in terms of the Cartan matrix of a 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.

22 pages, no figure, LaTeX: Introduction, Summary and Discussion are revised. (e-mail: [email protected])

References in corpus (3)

• Quantum Integrable Systems and Elliptic Solutions of Classical Discrete Nonlinear Equations
• Pfaffian and Determinant Solutions to A Discretized Toda Equation for $B_r,C_r$ and $D_r$
• Solutions of a discretized Toda field equation for $D_r$ from Analytic Bethe Ansatz

Cited by in corpus (7)

• T-systems and Y-systems in integrable systems
• Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1|s+1)
• Analytic Bethe ansatz related to a one parameter family of finite dimensional representations of the Lie superalgebra sl(r+1|s+1)
• Analytic Bethe ansatz and functional relations related to tensor-like representations of type II Lie superalgebras B(r|s) and D(r|s)
• Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time
• Analytic Bethe ansatz related to the Lie superalgebra C(s)
• T-systems and Y-systems for quantum affinizations of quantum Kac-Moody algebras