The moduli space of -flat connections

and the fusion rules

Author:
Masato Hayashi

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1545-1555

MSC (1991):
Primary 58D29, 57M05; Secondary 17B81, 17B10

Published electronically:
January 29, 1999

MathSciNet review:
1476136

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Abstract | References | Similar Articles | Additional Information

Abstract: The aim of this paper is to determine the existence condition of the moduli space of -flat connections on -holed -sphere , the so-called 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 PRV-conjecture.

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Additional Information

**Masato Hayashi**

Affiliation:
Department of Mathematical Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo

Email:
hayashim@ms318sun.ms.u-tokyo.ac.jp

DOI:
http://dx.doi.org/10.1090/S0002-9939-99-04674-2

Keywords:
Representations of the fundamental group of a surface,
Bruhat decomposition,
fusion rules,
PRV-conjecture

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