Skip to main content
SpringerLink
Log in

QuantumR matrix for the generalized Toda system

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We report the explicit form of the quantumR matrix in the fundamental representation for the generalized Toda system associated with non-exceptional affine Lie algebras.

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. Kulish, P. P., Sklyanin, E. K.: Solutions of the Yang-Baxter equation, J. Sov. Math.19, 1596 (1982)

    Google Scholar 

  2. Semenov-Tyan-Shanskii, M. A.: What is a classicalR-matrix? Funct. Anal. Appl.17, 259 (1983)

    Google Scholar 

  3. Drinfel'd, V. G.: Hamiltonian structures on Lie groups, Lie bi-algebras and the geometric meaning of the classical Yang-Baxter equations. Sov. Math. Dokl.27, 68 (1983)

    Google Scholar 

  4. Reshetikhin, N. Yu., Faddeev, L. D.: Hamiltonian structures for integrable models of field theory Theor. Math. Phys.56, 847 (1984)

    Google Scholar 

  5. Belavin, A. A., Drinfel'd, V. G.: Solutions of the classical Yang-Baxter equation for simple Lie algebras. Funct. Anal. Appl.16, 159 (1982)

    Google Scholar 

  6. Kulish, P. P., Reshetikhin, N. Yu., Sklyanin, E. K.: Yang-Baxter equation and representation theory I. Lett. Math. Phys.5, 393 (1981)

    Google Scholar 

  7. Kulish, P. P., Reshetikhin, N. Yu.: Quantum linear problem for the sine-Gordon equation and higher representations. J. Sov. Math.23, 2435 (1983)

    Google Scholar 

  8. Babelon, O., de Vega, H. J., Viallet, C. M.: Solutions of the factorization equations from Toda field theory. Nucl. Phys.B190, 542 (1981)

    Google Scholar 

  9. Cherednik, I. V.: On a method of constructing factorizedS matrices in elementary functions. Theor. Math. Phys.43, 356 (1980)

    Google Scholar 

  10. Chudnovsky, D. V., Chudnovsky, G. V.: Characterization of completelyX-symmetric factorizedS-matrices for a special type of interaction. Phys. Lett.79A, 36 (1980)

    Google Scholar 

  11. Schultz, C. L.: Solvableq-state models in lattice statistics and quantum field theory. Phys. Rev. Lett.46, 629 (1981)

    Google Scholar 

  12. Perk, J. H. H., Schultz, C. L.: New families of commuting transfer matrices inq-state vertex models. Phys. Lett.84A, 407 (1981)

    Google Scholar 

  13. Izergin, A. G., Korepin, V. E.: The inverse scattering method approach to the quantum Shabat-Mikhailov model. Commun. Math. Phys.79, 303 (1981)

    Google Scholar 

  14. Bogoyavlensky, O. I.: On perturbations of the periodic Toda lattice. Commun. Math. Phys.51, 201 (1976)

    Google Scholar 

  15. Olive, D. I., Turok, N.: Algebraic structure of Toda systems. Nucl. Phys.B220 [FS8], 491 (1983)

    Google Scholar 

  16. Kac, V. G.: Infinite dimensional Lie algebras. Boston, MA: Birkhäuser 1983

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. RIMS, Kyoto University, 606, Kyoto, Japan

    Michio Jimbo

Authors
  1. Michio Jimbo
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by H. Araki

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jimbo, M. QuantumR matrix for the generalized Toda system. Commun.Math. Phys. 102, 537–547 (1986). https://doi.org/10.1007/BF01221646

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01221646

Keywords

Search

Navigation