Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-10-25
J.Phys.Soc.Jap. 66 (1997) 3391-3398
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, no figure, LaTeX: Introduction, Summary and Discussion are revised. (e-mail: ss57058@hongo.ecc.u-tokyo.ac.jp)
Scientific paper
10.1143/JPSJ.66.3391
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.
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