The moduli space of flat connections and the fusion rules
Author:
Masato Hayashi
Journal:
Proc. Amer. Math. Soc. 127 (1999), 15451555
MSC (1991):
Primary 58D29, 57M05; Secondary 17B81, 17B10
Published electronically:
January 29, 1999
MathSciNet review:
1476136
Fulltext PDF Free Access
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Abstract: The aim of this paper is to determine the existence condition of the moduli space of flat connections on holed sphere , the socalled pair of pants, and to study its relationship to the fusion rules. The existence condition can be expressed by a system of inequalities with the entries of highest weights with respect to the fundamental weights. This gives a necessary condition for the fusion coefficents to be nontrivial. We also find that the fusion coefficient of a triplet of extremal highest weights equals one. This can be considered a quantum counterpart of the PRVconjecture.
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Additional Information
Masato Hayashi
Affiliation:
Department of Mathematical Sciences, University of Tokyo, Komaba, Meguroku, Tokyo
Email:
hayashim@ms318sun.ms.utokyo.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993999046742
PII:
S 00029939(99)046742
Keywords:
Representations of the fundamental group of a surface,
Bruhat decomposition,
fusion rules,
PRVconjecture
Received by editor(s):
May 13, 1996
Received by editor(s) in revised form:
September 3, 1997
Published electronically:
January 29, 1999
Communicated by:
Ronald A. Fintushel
Article copyright:
© Copyright 1999
American Mathematical Society
