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Combinatorics, Bethe Ansatz, and representations of the symmetric group. (English) Zbl 0639.20028
Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 155, 50-64 (Russian) (1986; Zbl 0617.20024).

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
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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
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