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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Reciprocity Laws in the Verlinde Formulae
for the Classical Groups


Authors: W. M. Oxbury and S. M. J. Wilson
Journal: Trans. Amer. Math. Soc. 348 (1996), 2689-2710
MSC (1991): Primary 14D20, 14H15
MathSciNet review: 1340183
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Abstract: The Verlinde formula is computed for each of the simply-connected classical Lie groups, and it is shown that the resulting formula obeys certain reciprocity laws with respect to the exchange of the rank and the level. Some corresponding dualities between spaces of sections of theta line bundles over moduli spaces of $G$-bundles on curves are conjectured but not proved.


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Additional Information

W. M. Oxbury
Affiliation: Department of Mathematical Sciences, Science Laboratories, South Road, Durham DH1 3LE, U.K.
Email: w.m.oxbury@durham.ac.uk

S. M. J. Wilson
Affiliation: Department of Mathematical Sciences, Science Laboratories, South Road, Durham DH1 3LE, U.K.
Email: s.m.j.wilson@durham.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01563-2
PII: S 0002-9947(96)01563-2
Received by editor(s): March 6, 1995
Received by editor(s) in revised form: May 21, 1995
Article copyright: © Copyright 1996 American Mathematical Society