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), 26892710
MSC (1991):
Primary 14D20, 14H15
MathSciNet review:
1340183
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Abstract: The Verlinde formula is computed for each of the simplyconnected 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 bundles on curves are conjectured but not proved.
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A. Szenes, The combinatorics of the Verlinde formulas (N.J. Hitchin et al., ed.), in Vector bundles in algebraic geometry, Cambridge, 1995.
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D. Zagier, Elementary aspects of the Verlinde formula and of the HarderNarasimhanAtiyahBott formula, preprint, 1994.
 [B1]
 A. Beauville, Vector bundles on curves and generalised theta functions: recent results and open problems, preprint, 1994.
 [B2]
 , Conformal blocks, fusion rules and the Verlinde formula, preprint, 1994.
 [DT]
 R. Donagi, L.W. Tu, Theta functions for versus , Math. Research Letters 1 (1994), 345357. MR 95j:14012
 [F]
 G. Faltings, A proof for the Verlinde formula, J. Alg. Geometry 3 (1994), 347374. MR 95j:14013
 [FH]
 W. Fulton, J. Harris, Representation theory, Springer, 1991. MR 93a:20069
 [K]
 V.G. Kac, Infinite dimensional Lie algebras, 3rd edition, Cambridge, 1990. MR 92k:17038
 [KNR]
 S. Kumar, M.S. Narasimhan, A. Ramanathan, Infinite Grassmannian and moduli space of bundles, Math. Annalen 300 (1994), 4175. MR 96e:14011
 [O]
 W.M. Oxbury, Prym varieties and the moduli of spin bundles, to appear in proceedings of the Annual Europroj Conference, Barcelona, 1994.
 [Sz]
 A. Szenes, The combinatorics of the Verlinde formulas (N.J. Hitchin et al., ed.), in Vector bundles in algebraic geometry, Cambridge, 1995.
 [Z]
 D. Zagier, Elementary aspects of the Verlinde formula and of the HarderNarasimhanAtiyahBott formula, preprint, 1994.
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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/S0002994796015632
PII:
S 00029947(96)015632
Received by editor(s):
March 6, 1995
Received by editor(s) in revised form:
May 21, 1995
Article copyright:
© Copyright 1996
American Mathematical Society
