Skip to main content
SpringerLink
Log in

Bosonic Formulas for (k, l)-Admissible Partitions

  • Published:
The Ramanujan Journal Aims and scope Submit manuscript

Abstract

Bosonic formulas for generating series of partitions with certain restrictions are obtained by solving a set of linear matrix q-difference equations. Some particular cases are related to combinatorial problems arising from solvable lattice models, representation theory and conformal field theory.

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. R. Baxter, Exactly Solved Models in Statistical Mechanics, Academic Press, London, 1982.

    Google Scholar 

  2. A. Berkovich, B. McCoy, and A. Schilling, “Rogers-Schur-Ramanujan type identities for the M(p, p') minimal models of conformal field theory,” Commun. Math. Phys. 191 (1998), 325–395.

    Google Scholar 

  3. B. Feigin, M. Jimbo, and T. Miwa, “Vertex operator algebra arising from the minimal series M(3, p) and monomial basis,” in MathPhys Odyssey 2001: Integrable Models and Beyond. In Honor of Barry M. McCoy (M. Kashiwara and T. Miwa, eds.), Birkhauser, Boston, 2002.

    Google Scholar 

  4. B. Feigin and S. Loktev, “On finitization of the Gordon identities,” math.QA/0006221.

  5. B. Feigin and A. Stoyanovsky, “Quasi-particles models for the representations of Lie algebras and geometry of flag manifold, hep-th/9308079, RIMS 942; Functional models for the representations of current algebras and the semi-infinite Schubert cells,” Funct. Anal. Appl. 28 (1994), 55–72.

    Google Scholar 

  6. M. Jimbo, T. Miwa, and E. Mukhin, “Bosonic formula for sl 2 coinvariants, math. QA/0107053.

  7. A. Pukhlikov and A. Khovanskii, “Finitely additive measures of virtual polytopes,” St. Petersburg Math J. 4 (1993), 337–356.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Landau Institute for Theoretical Physics, Chernogolovka, 142432, Russia

    B. Feigin

  2. Graduate School of Mathematical Sciences, University of Tokyo, Tokyo, 153-8914, Japan

    M. Jimbo

  3. Independent University of Moscow, B. Vlasievsky per, 11, Moscow

    S. Loktev

  4. Division of Mathematics, Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan

    T. Miwa

  5. Department of Mathematics, University of California, Berkeley, California, 94720

    E. Mukhin

Authors
  1. B. Feigin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Jimbo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Loktev
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. T. Miwa
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. E. Mukhin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feigin, B., Jimbo, M., Loktev, S. et al. Bosonic Formulas for (k, l)-Admissible Partitions. The Ramanujan Journal 7, 485–517 (2003). https://doi.org/10.1023/B:RAMA.0000012430.68976.c0

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:RAMA.0000012430.68976.c0

Search

Navigation