Reciprocity Laws in the Verlinde Formulae for the Classical Groups
HTML articles powered by AMS MathViewer
- by W. M. Oxbury and S. M. J. Wilson PDF
- Trans. Amer. Math. Soc. 348 (1996), 2689-2710 Request permission
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.References
- A. Beauville, Vector bundles on curves and generalised theta functions: recent results and open problems, preprint, 1994.
- —, Conformal blocks, fusion rules and the Verlinde formula, preprint, 1994.
- L. Kantorovitch, The method of successive approximations for functional equations, Acta Math. 71 (1939), 63–97. MR 95, DOI 10.1007/BF02547750
- Hidegorô Nakano, Über Abelsche Ringe von Projektionsoperatoren, Proc. Phys.-Math. Soc. Japan (3) 21 (1939), 357–375 (German). MR 94
- William Fulton and Joe Harris, Representation theory, Graduate Texts in Mathematics, vol. 129, Springer-Verlag, New York, 1991. A first course; Readings in Mathematics. MR 1153249, DOI 10.1007/978-1-4612-0979-9
- Victor G. Kac, Infinite-dimensional Lie algebras, 3rd ed., Cambridge University Press, Cambridge, 1990. MR 1104219, DOI 10.1017/CBO9780511626234
- Hidegorô Nakano, Über Abelsche Ringe von Projektionsoperatoren, Proc. Phys.-Math. Soc. Japan (3) 21 (1939), 357–375 (German). MR 94
- W.M. Oxbury, Prym varieties and the moduli of spin bundles, to appear in proceedings of the Annual Europroj Conference, Barcelona, 1994.
- A. Szenes, The combinatorics of the Verlinde formulas (N.J. Hitchin et al., ed.), in Vector bundles in algebraic geometry, Cambridge, 1995.
- D. Zagier, Elementary aspects of the Verlinde formula and of the Harder-Narasimhan-Atiyah-Bott formula, preprint, 1994.
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
- Received by editor(s): March 6, 1995
- Received by editor(s) in revised form: May 21, 1995
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 348 (1996), 2689-2710
- MSC (1991): Primary 14D20, 14H15
- DOI: https://doi.org/10.1090/S0002-9947-96-01563-2
- MathSciNet review: 1340183