Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu. Combinatorics, Bethe Ansatz, and representations of the symmetric group. (English) Zbl 0639.20028 J. Sov. Math. 41, No. 2, 916-924 (1988). Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 155, 50-64 (Russian) (1986; Zbl 0617.20024). Cited in 4 ReviewsCited in 22 Documents MSC: 20G45 Applications of linear algebraic groups to the sciences 22E70 Applications of Lie groups to the sciences; explicit representations 05A17 Combinatorial aspects of partitions of integers 20C30 Representations of finite symmetric groups 05A05 Permutations, words, matrices Keywords:Young diagram; representations of symmetric groups; quantum inverse scattering; standard Young tableaux; rigged configurations; integrable quantum system PDF BibTeX XML Cite \textit{S. V. Kerov} et al., J. Sov. Math. 41, No. 2, 916--924 (1988; Zbl 0639.20028) Full Text: DOI References: [1] H. Bethe, ?Zur Theorie der Metalle. I. Eigenwerte und Eigenfunktionen der linearen Atom Kette,? Z. Physik,71, 205?226 (1931). · JFM 57.1587.01 · doi:10.1007/BF01341708 [2] L. A. Takhtadzhyan and L. D. Faddeev, ?Spectrum and scattering of stimuli in one-dimensional Heisenberg magnetics,? in: Differential Geometry, Lie Groups, and Mechanics. IV, J. Sov. Math.,24, No. 2 (1984). · Zbl 0532.47009 [3] A. N. Kirillov, ?Combinatorial identities and completeness of states of Heisenberg magnetics,? in: Questions of Quantum Field Theory and Statistical Physics. 4, J. Sov. Math.,30, No. 4 (1985). [4] A. N. Kirillov, ?Completeness of states of generalized Heisenberg magnetics,? in: Automorphic Functions and Number Theory. II, J. Sov. Math.,36, No. 1 (1987). [5] I. MacDonald, Symmetric Functions and Hall Polynomials [Russian translation], Moscow (1985). · Zbl 0672.20007 [6] D. Knuth, The Art of Computer Programming [Russian translation], Vol. 3, Moscow (1978). [7] S. V. Kerov and A. M. Vershik, ?The characters of the infinite symmetric group and probability properties of the Robinson-Schensted-Knuth algorithm,? SIAM J. Alg. Disc. Math.,7, No. 1, 116?124 (1986). · Zbl 0584.05004 · doi:10.1137/0607014 [8] A. N. Kirillov and N. Yu. Reshetikhin, ?The Yangians, Bethe Ansatz and combinatorics,? Preprint, 1986. · Zbl 0643.20027 [9] P. P. Kulish and N. Yu. Reshetikhin, ?Diagonalization of GL(N) invariant transfer matrices and quantum N-wave system (Lee model),? J. Phys. A,16, 591?596. [10] A. N. Kirillov and N. Yu. Reshetikhin, ?Bethe Ansatz and combinatorics of Young tableaux,? this issue, pp. 65?115. · Zbl 0617.20025 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.