Skip to main content
Log in

QuantumR matrices related to the spin representations ofB n andD n

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

Abstract

We present the explicit form of the trigonometricR matrices related to the spin representations of the simple Lie algebrasX n=B n,D n. We conjecture that one dimensional configuration sums of the corresponding vertex models in the face formulation are the string functions ofX (1) n modules.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Drinfeld, V. G.: Quantum groups. In: Proceedings of the International Congress of Mathematicians. pp. 798–820. New York: Berkeley 1986

    Google Scholar 

  2. Kulish, P. P., Reshetikhin, N. Yu.: Quantum linear problem for the sine-Gordon equation and higher representations. J. Sov. Math.23, 2435–2441 (1983); Sogo, K., Akutsu, Y., Abe, T.: New factorizedS-matrix and its application to exactly solvableq-state model I. Prog. Theor. Phys.70, 730–738 (1983), II. ibid. 739–746; Jimbo, M.: Aq-difference analogue ofU(g) and the Yang-Baxter equation. Lett. Math. Phys.10, 63–69 (1985)

    Article  Google Scholar 

  3. Kulish, P. P., Reshetikhin, N. Yu., Sklyanin, E. K.: Yang-Baxter equation and representation theory I. Lett. Math. Phys.5, 393–403 (1981)

    Article  Google Scholar 

  4. Bazhanov, V. V.: Trigonometric solutions of triangle equations and classical Lie algebras. Phys. Lett.B159, 321–324 (1985), Integrable quantum systems and classical Lie algebras. Commun. Math. Phys.113, 471–503 (1987)

    Article  Google Scholar 

  5. Jimbo, M.: QuantumR matrix for the generalized Toda system. Commun. Math. Phys.102, 537–547 (1986)

    Article  Google Scholar 

  6. Kuniba, A.: QuantumR matrix forG 2 and a solvable 173 vertex model. J. Phys. A: Math. Gen.23, 1349–1362 (1990)

    Article  Google Scholar 

  7. Cherednik, I. V.: On “quantum” deformations of irreducible finite-dimensional representations of gI N . Sov. Math. Dokl.33, 507–510 (1986)

    Google Scholar 

  8. Date, E., Jimbo, M., Kuniba, A., Miwa, T., Okado, M.: Exactly solvable SOS models: Local height probabilities and theta function identities. Nucl. Phys.B290[FS20], 231–273 (1987)

    Article  Google Scholar 

  9. Jimbo, M., Miwa, T., Okado, M.: Local state probabilities of solvable lattice models: AnA (1) n−1 family. Nucl. Phys.300[FS22], 74–108 (1988)

    Article  Google Scholar 

  10. Baxter, R. J.: Exactly solved models in statistical mechanics. London: Academic Press 1982

    Google Scholar 

  11. Date, E., Jimbo, M., Kuniba, A., Miwa, T., Okado, M.: One-dimensional configuration sums in vertex models and affine Lie algebra characters. Lett. Math. Phys.17, 69–77 (1989)

    Article  Google Scholar 

  12. Kac, V. G., Peterson, D. H.: Infinite-dimensional Lie algebras, theta functions and modular forms. Adv. Math.53, 125–264 (1984)

    Article  Google Scholar 

  13. Reshetikhin, N. Yu.: Algebraic Bethe Ansatz for theSO(n) invariant transfer-matrices. Zapiski nauch. LOMI169, 122–140 (1988) (in Russian)

    Google Scholar 

  14. Reshetikhin, N. Yu.: Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links I. preprint LOMI E-4-87 1988

  15. Lusztig, G.: Quantum deformations of certain simple modules over enveloping algebras. Adv. Math.70, 237–249 (1988); Rosso, M.: Finite-dimensional representations of quantum analog of the enveloping algebra of a complex simple Lie algebra. Commun. Math. Phys.117, 581–593 (1988)

    Article  Google Scholar 

  16. Kac, V. G.: Infinite dimensional Lie algebras. Cambridge: Cambridge University Press 1985

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by H. Araki

Rights and permissions

Reprints and permissions

About this article

Cite this article

Okado, M. QuantumR matrices related to the spin representations ofB n andD n . Commun.Math. Phys. 134, 467–486 (1990). https://doi.org/10.1007/BF02098442

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02098442

Keywords

Navigation