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Letters in Mathematical Physics

, Volume 17, Issue 1, pp 69–77 | Cite as

One-dimensional configuration sums in vertex models and affine Lie algebra characters

  • E. Date
  • M. Jimbo
  • A. Kuniba
  • T. Miwa
  • M. Okado
Article

Abstract

We study the local state probabilities of the vertex models in the face formulation associated with the simple Lie algebras Xn=An, Bn, Cn, Dn. The corner transfer matrix method expresses them in terms of one-dimensional configuration sums. We show that the latter are the string functions of Xn(1) modules. We also present similar results for the restricted face models of types Bn(1), Cn(1), Dn(1).

AMS subject classifications (1980)

17B67 82A05 

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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • E. Date
    • 1
  • M. Jimbo
    • 2
  • A. Kuniba
    • 3
  • T. Miwa
    • 2
  • M. Okado
    • 2
  1. 1.Department of Mathematics, College of General EducationKyoto UniversityKyotoJapan
  2. 2.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  3. 3.Institute of Physics, College of Arts and SciencesUniversity of TokyoTokyoJapan

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