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Functional Analysis and Its Applications

, Volume 48, Issue 3, pp 175–182 | Cite as

Commutative vertex algebras and their degenerations

  • B. L. FeiginEmail author
Article
  • 99 Downloads

Abstract

Commutative vertex algebras arising as subalgebras of the vertex algebras corresponding to the Kac-Moody algebras are studied. Systems of defining relations and degenerations into algebras with quadratic relations are described. The results can be used to obtain fermionic formulas for characters.

Key words

vertex algebras Abelianization quadratic algebras 

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References

  1. [1]
    B. L. Feigin and E. B. Feigin, “Integrable \(\widehat{sl}_2\)-modules as infinite tensor products,” in: Fundamental Mathematics Today [in Russian], NTsNMO, Moscow, 2003, 304–334.Google Scholar
  2. [2]
    B. Feigin and A. Stoyanovsky, Quasi-particles models for the representations of Lie algebras and geometry of flag manifold, http://xxx.lanl.gov/abs/hep-th/9308079.
  3. [3]
    A. V. Stoyanovskii and B. L. Feigin,, “Functional models for 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. Soviet Math., vol. 16, Part 1, Amer. Math. Soc., Providence, RI, 1993, 139–148.Google Scholar
  5. [5]
    B. Feigin and S. Loktev, “On generalized Kostka polynomials and the quantum Verlinde rule,” in: Differential Topology, Infinite-Dimensional Lie Algebras, and Applications, Amer. Math. Soc. Transl. Ser. 2, vol. 194, Amer. Math. Soc., Providence, RI, 1999, 61–79; http://arxiv.org/abs/math/9812093.Google Scholar
  6. [6]
    I. B. Frenkel and V. G. Kac, “Basic representations of affine Lie algebras and dual resonance models,” Invent. Math., 62:1 (1980), 23–66.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    B. L. Feigin, M. Jimbo, T. Miwa, E. Mukhin, and Y. Takeyama, “Fermionic formulas for (k, 3)-admissible configurations,” Publ. Res. Inst. Math. Sci., 40:1 (2004), 125–162.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    V. Kac, Vertex Algebras for Beginners, University Lecture Series, vol. 10, Amer. Math. Soc., Providence, RI, 1998.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsNational Research University “Higher School of Economics”MoscowRussia

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