Functional Analysis and Its Applications

, Volume 45, Issue 4, pp 297–304 | Cite as

Abelianization of the BGG resolution of representations of the Virasoro algebra

Article

Abstract

We construct a resolution that permits computing the t-character of representations of the Virasoro algebra from the (2, 2p + 1)-models, i.e., the characters of the associated graded spaces with respect to the Poincaré-Birkhoff-Witt filtration.

Key words

Virasoro algebra t-characters of irreducible representations abelianization 

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References

  1. [1]
    G. E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, 1976.Google Scholar
  2. [2]
    B. Feigin and A. Stoyanovsky, Quasi-particles models for the representations of Lie algebras and geometry of flag manifold, RIMS-942, http://xxx.lanl.gov/abs/hep-th/9308079.
  3. [3]
    B. L. Feigin and A. V. Stoyanovskii, “Functional models of the representations of current algebras, and semi-infinite Schubert cells,” Funkts. Anal. Prilozhen., 28:1 (1994), 68–90; English transl.: Functional Anal. Appl., 28:1 (1994), 55–72.MathSciNetGoogle Scholar
  4. [4]
    B. Feigin and E. Frenkel, “Coinvariants of nilpotent subalgebras of the Virasoro algebra and partition identities,” in: I. M. Gelfand Seminar, Adv. in Soviet Math., vol. 16, Part 1, Amer. Math. Soc., Providence, RI, 1993, 139–148.Google Scholar
  5. [5]
    G. Felder, “BRST approach to minimal models,” Nuclear Phys. B, 317:1 (1989), 215–236.CrossRefMathSciNetGoogle Scholar
  6. [6]
    E. Feigin, G. Fourier, and P. Littelmann, “PBW filtration and bases for irreducible modules in type A n,” Transformation Groups, 16:1 (2011), 71–89.CrossRefMATHMathSciNetGoogle Scholar
  7. [7]
    A. Rocha-Caridi, “Vacuum vector representations of the Virasoro algebra,” in: Vertex Operators in Mathematical Physics (Berkeley, Calif., 1983), Math. Sci. Res. Inst. Publ., vol. 3, Springer-Verlag, New York, 1985, 451–473.Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsHigher School of Economics (National Research University)MoscowRussia

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