Letters in Mathematical Physics

, Volume 28, Issue 4, pp 257–268

Berenstein-Zelevinsky triangles, elementary couplings, and fusion rules

  • L. Begin
  • A. N. Kirillov
  • P. Mathieu
  • M. A. Walton
Article

DOI: 10.1007/BF00761494

Cite this article as:
Begin, L., Kirillov, A.N., Mathieu, P. et al. Lett Math Phys (1993) 28: 257. doi:10.1007/BF00761494

Abstract

We present a general scheme for describing\(\widehat{su}\)(N)k fusion rules in terms of elementary couplings, using Berenstein-Zelevinsky triangles. A fusion coupling is characterized by its corresponding tensor product coupling (i.e. its Berenstein-Zelevinsky triangle) and the threshold level at which it first appears. We show that a closed expression for this threshold level is encoded in the Berenstein-Zelevinsky triangle and an explicit method to calculate it is presented. In this way, a complete solution of\(\widehat{su}\)(4)k fusion rules is obtained.

Mathematics Subject Classification (1991)

81-XX 

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • L. Begin
    • 1
  • A. N. Kirillov
    • 2
  • P. Mathieu
    • 1
  • M. A. Walton
    • 3
  1. 1.Département de PhysiqueUniversité LavalQuébecCanada
  2. 2.Steklov Mathematical InstituteSt. PetersburgRussia
  3. 3.Physics DepartmentUniversity of LethbridgeAlbertaCanada

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