zbMATH — the first resource for mathematics

Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras. (English. Russian original) Zbl 0900.16047
Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 160, 211–221 (1987; Zbl 0637.16007).

16T20 Ring-theoretic aspects of quantum groups
17B37 Quantum groups (quantized enveloping algebras) and related deformations
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
Full Text: DOI
[1] L. D. Fadeev, ”Integrable models in (1+1)-dimensional quantum field theory”, in: Recent Advances in Field Theory and Statistical Mechanics (Les Houches, 1982), North-Holland, Amastedam (1984), pp. 561–608.
[2] L. D. Faddeev and L. A. Takhtadzhya, ”The quantum method for the inverse problem and the XYZ Heisenberg model”, Usp. Mat. Nauk,34, No. 5, 13–63 (1979).
[3] E. K. Sklyanin, ”Quantum variant of the method of the inverse scattering problem”, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,95, 55–128 (1980). · Zbl 0464.35071
[4] V. G. Drinfel’d, ”Hopf algebras and the Yang-Baxter quantum equation”, Dokl. Akad. Nauk SSSR,283, No. 5, 1060–1064 (1985).
[5] V. G. Drinfel’d, ”Quantum groups”, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,155, 18–49 (1986).
[6] V. E. Korepin, ”Analysis of the bilinear relation of a six-vertex model”, Dokl. Akad. Nauk SSSR,265, No. 6, 1361–1364 (1982).
[7] P. P. Kulish, N. Yu. Reshetikhin, E. K. Sklyanin, ”Yang-Baxter equation and representation theory: I.”, Lett. Math. Phys.,5, No. 5, 393–403 (1981). · Zbl 0502.35074 · doi:10.1007/BF02285311
[8] V. O. Tarasov, ”On the structure of quantum L-operators for the R-matrix of the XXZ-model”, Teor. Mat. Fiz.,61, No. 2, 163–173 (1984).
[9] V. G. Drinfel’d, A new realization of Yangians in quantum affine algebras. Preprint No. 30-86, FTINT, Akad. Nauk Ukrain. SSR, Kharkov (1986).
[10] N. Yu. Reshetikhin, ”Integrable models of quantum one-dimensional magnets with O(n)-and Sp(2k)-symmetries”, Teor. Mat. Fiz.,63, No. 3, 347–366 (1985).
[11] E. Ogievetsky and P. Wiegmann, ”Factorized S-matrix and the Bethe ansatz for simple Lie groups”, Phys. Lett. B,168, No. 4, 360–366 (1986). · doi:10.1016/0370-2693(86)91644-8
[12] A. N. Kirillov, ”Combinatorial identities and completeness of states of the Heisenberg magnet”, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,131, 88–105 (1983).
[13] A. N. Kirillov, ”Completeness of states of the generalized Heisenberg magnet”, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,134, 169–189 (1984). · Zbl 0538.58016
[14] A. N. Kirillov and N. Yu. Reshetikhin, ”The Bethe ansatz and the combinatorics of Young tableaux”, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,155, 65–115 (1986). · Zbl 0617.20025
[15] S. V. Kerov, A. N. Kirillov, and N. Yu. Reshetikhin, ”Combinatorics, the Bethe ansatz and representations of the symmetric group”, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,155, 50–64 (1986). · Zbl 0617.20024
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.