Skip to main content
SpringerLink
Log in

Commutative vertex algebras and their degenerations

  • Published:
Functional Analysis and Its Applications Aims and scope

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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. 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. 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.

    MathSciNet  Google Scholar 

  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. 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. I. B. Frenkel and V. G. Kac, “Basic representations of affine Lie algebras and dual resonance models,” Invent. Math., 62:1 (1980), 23–66.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  8. V. Kac, Vertex Algebras for Beginners, University Lecture Series, vol. 10, Amer. Math. Soc., Providence, RI, 1998.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Landau Institute for Theoretical Physics, National Research University “Higher School of Economics”, Moscow, Russia

    B. L. Feigin

Authors
  1. B. L. Feigin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. L. Feigin.

Additional information

Dedicated to the memory of I. M. Gelfand

__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 48, No. 3, pp. 24–33, 2014

Original Russian Text Copyright © by B. L. Feigin

This work was supported in part by RFBR grant nos. 13-01-12401-ofi_m and 12-01-00836-a. This study was carried out within the National Research University Higher School of Economics’ Academic Fund Program in 2013–2014, research grant no. 12-01-0016.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Feigin, B.L. Commutative vertex algebras and their degenerations. Funct Anal Its Appl 48, 175–182 (2014). https://doi.org/10.1007/s10688-014-0059-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10688-014-0059-7

Key words

Search

Navigation