Mathematical Aspects of the Verlinde Formula

  • M. Schottenloher
Part of the Lecture Notes in Physics book series (LNP, volume 759)


Modulus Space Vector Bundle Line Bundle Conjugacy Class Marked Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [APW91]
    S. Axelrod, S. Della Pietra, and E. Witten. Geometric quantization of Chern-Simons gauge theory. J. Diff. Geom. 33 (1991), 787–902.zbMATHMathSciNetGoogle Scholar
  2. [BK01*]
    B. Bakalov and A. Kirillov, Jr. Lectures on Tensor Categories and Modular Functors, AMS University Lecture Series 21, AMS, Providence, RI, 2001.Google Scholar
  3. [Bea95]
    A. Beauville. Vector bundles on curves and generalized theta functions: Recent results and open problems. In: Current Topics in Complex Algebraic Geometry. Math. Sci. Res. Inst. Publ. 28, 17–33, Cambridge University Press, Cambridge, 1995.Google Scholar
  4. [Bea96]
    A. Beauville. Conformal blocks, fusion rules and the Verlinde formula. In: Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry (Ramat Gan, 1993), 75–96, Bar-Ilan University, Ramat Gan, 1996.Google Scholar
  5. [BF01*]
    D. Ben-Zvi and E. Frenkel. Vertex Algebras and Algebraic Curves. AMS, Providence, RI, 2001.zbMATHGoogle Scholar
  6. [BT93]
    M. Blau and G. Thompson. Derivation of the Verlinde formula from Chern-Simons theory. Nucl. Phys. B 408 (1993), 345–390.CrossRefADSMathSciNetGoogle Scholar
  7. [Bot91]
    R. Bott. Stable bundles revisited. Surveys in Differential Geometry (Supplement to J. Diff. Geom.) 1 (1991), 1–18.ADSMathSciNetGoogle Scholar
  8. [Fal94]
    G. Faltings. A proof of the Verlinde formula. J. Alg. Geom. 3 (1994), 347–374.zbMATHMathSciNetGoogle Scholar
  9. [Fal08*]
    G. Faltings. Thetafunktionen auf Modulräumen von Vektorbündeln. Jahresbericht der DMV 110 (2008), 3–18.MathSciNetzbMATHGoogle Scholar
  10. D. Freed, M. Hopkins, and C. Teleman. Loop groups and twisted K-theory III. arXiv:math/0312155v3 (2003).Google Scholar
  11. [Fuc92]
    J. Fuchs. Affine Lie Algebras and Quantum Groups. Cambridge University Press, Cambridge, 1992.zbMATHGoogle Scholar
  12. [Hit90]
    N. Hitchin. Flat connections and geometric quantization. Comm. Math. Phys. 131 (1990), 347–380.zbMATHCrossRefADSMathSciNetGoogle Scholar
  13. [HJJS08*]
    Husemöller, D., Joachim, M., Jurco, B., Schottenloher, M.: Basic Bundle Theory and K-Cohomological Invariants. Lect. Notes Phys. 726. Springer, Heidelberg (2008)Google Scholar
  14. [Kac90]
    V. Kac. Infinite Dimensional Lie Algebras. Cambridge University Press, Cambridge, 3rd ed., 1990.zbMATHCrossRefGoogle Scholar
  15. [Kir76]
    A. A. Kirillov. Theory of Representations. Springer Verlag, Berlin, 1976.zbMATHGoogle Scholar
  16. [KNR94]
    S. Kumar, M. S. Narasimhan, and A. Ramanathan. Infinite Grassmannians and moduli spaces of G-bundles. Math. Ann. 300 (1994), 41–75.zbMATHCrossRefMathSciNetGoogle Scholar
  17. [MS80]
    V. Mehta and C. Seshadri. Moduli of vector bundles on curves with parabolic structures. Ann. Math. 248 (1980), 205–239.zbMATHCrossRefMathSciNetGoogle Scholar
  18. [Mic05*]
    J. Mickelsson. Twisted K Theory Invariants. Letters in Mathematical Physics 71 (2005), 109–121.zbMATHCrossRefADSMathSciNetGoogle Scholar
  19. [MS89]
    G. Moore and N. Seiberg. Classical and conformal field theory. Comm. Math. Phys. 123 (1989), 177–254.zbMATHCrossRefADSMathSciNetGoogle Scholar
  20. [NR93]
    M.S. Narasimhan and T. Ramadas. Factorization of generalized theta functions I. Invent. Math. 114 (1993), 565–623.zbMATHCrossRefADSMathSciNetGoogle Scholar
  21. [NS65]
    M.S. Narasimhan and C. Seshadri. Stable and unitary vector bundles on a compact Riemann surface. Ann. Math. 65 (1965), 540–567.MathSciNetCrossRefGoogle Scholar
  22. T. Ramadas. Factorization of generalized theta functions II: The Verlinde formula. Preprint, 1994.Google Scholar
  23. [Sche92]
    P. Scheinost. Metaplectic quantization of the moduli spaces of at and parabolic bundles. Dissertation, LMU München, 1992.Google Scholar
  24. [ScSc95]
    P. Scheinost and M. Schottenloher. Metaplectic quantization of the moduli spaces of at and parabolic bundles. J. Reine Angew. Math. 466 (1995), 145–219.zbMATHMathSciNetGoogle Scholar
  25. C. Sorger. La formule de Verlinde. Preprint, 1995. (to appear in Sem. Bourbaki, année 1994–95, no 793)Google Scholar
  26. [Sze95]
    A. Szenes. The combinatorics of the Verlinde formula. In: Vector Bundles in Algebraic Geometry, Hitchin et al. (Eds.), 241–254. Cambridge University Press, Cambridge, 1995.Google Scholar
  27. [TUY89]
    A. Tsuchiya, K. Ueno, and Y. Yamada. Conformal field theory on the universal family of stable curves with gauge symmetry. In: Conformal field theory and solvable lattice models. Adv. Stud. Pure Math. 16 (1989), 297–372.Google Scholar
  28. [Tur94]
    V.G. Turaev. Quantum Invariants of Knots and 3-Manifolds. DeGruyter, Berlin, 1994.zbMATHGoogle Scholar
  29. [Tyu03*]
    A. Tyurin. Quantization, Classical and Quantum Field Theory and Theta Functions, CRM Monograph Series 21 AMS, Providence, RI, 2003.zbMATHGoogle Scholar
  30. [Uen95]
    K. Ueno. On conformal field theory. In: Vector Bundles in Algebraic Geometry, N.J. Hitchin et al. (Eds.), 283–345. Cambridge University Press, Cambridge, 1995.Google Scholar
  31. [Ver88]
    E. Verlinde. Fusion rules and modular transformations in two-dimensional conformal field theory. Nucl. Phys. B 300 (1988), 360–376.CrossRefADSMathSciNetGoogle Scholar
  32. [Wit89]
    E. Witten. Quantum field theory and the Jones polynomial. Commun. Math. Phys. 121 (1989), 351–399.zbMATHCrossRefADSMathSciNetGoogle Scholar
  33. [Wit93*]
    E. Witten. The Verlinde algebra and the cohomology of the Grassmannian. hep-th/9312104 In: Geometry, Topology and Physics, Conf. Proc.Lecture Notes in Geom. Top, 357–422. Intern. Press, Cambridge MA (1995).Google Scholar
  34. [Woo80]
    N. Woodhouse. Geometric Quantization. Clarendon Press, Oxford, 1980.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • M. Schottenloher
    • 1
  1. 1.Ludwig-Maximilians-Universitä München80333 MünchenGermany

Personalised recommendations