The Bethe Ansatz and the combinatorics of Young tableaux

I. MacDonald, Symmetric Functions and Hall Polynomials [Russian translation], Moscow (1985).

G. James, Theory of Representations of the Symmetric Group [Russian translation], Moscow (1982).

D. P. Zhelobenko, Compact Lie Groups and Their Representations [in Russian], Moscow (1970).

N. Bourbaki, Lie Groups and Algebras [Russian translation], Moscow (1972).

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. Discr. Math.,7, 116?124 (1986).

A. N. Sergeev, ?Tensor algebra of the identity representation as a module over the Lie superalgebras gl(N/M) and Q(N),? Mat. Sb.,124, 422?430 (1984).

A. Berele and J. Regev, ?Hook Young diagrams with applications to combinatorics and to representation of Lie superalgebras,? Adv. Math.

A. Berele and J. Remm, ?Hook flag characters and their combinatorics,? J. Pure Appl. Algebra,35, 225?245 (1985).

J. Frame, G. Robinson, and R. Thrall, ?The hook graphs,? Can. J. Math.,6, 316?324 (1954).

V. Kac, ?Lie superalgebras,? Adv. Math.,26, No. 1, 8?96 (1977).

G. Lusztig, ?Green polynomials and singularities of unipotent classes,? Adv. Math.,42, 173?204 (1981).

G. Lusztig, ?Singularities, character formula and q-analog of weight multiplicity,? Asterisque,101, 120?130.

I. M. Gel'fand and A. V. Zelevinskii, ?Polyhedra in the space of schemes and canonical basis in irreducible representations of gl3,? Funkts. Anal. Prilozhen.,19, No. 2, 72?75 (1985).

I. M. Gel'fand and A. V. Zelevinskii, Materials of the Seminar in Yurmal' [in Russian] (1985).

A. Lascoux and M. P. Schützenberger, Asterisque,87?88, 249?266 (1981).

A. Lascoux and M. P. Schützenberger, ?Sur une conjecture de H. O. Foulkes,? C. R. Acad. Sci. Paris,286A, 323?324 (1978).

G. Thomas, ?Further result on Baxter sequences and generalized Schur functions,? Lect. Notes Math.,579, 155?167 (1976).

D. A. Leites, ?Introduction to the theory of supermanifolds,? Usp. Mat. Nauk,35, No. 1, 3?57 (1980).

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).

A. N. Kirillov, ?Completeness of states of generalized Heisenberg magnetics,? in: Automorphic Functions and Number Theory. 11, J. Sov. Math.,36, No. 1 (1987).

A. N. Kirillov and N. Yu. Reshetikhin, ?Yangians, Bethe-Ansatz and combinatorics,? Lett. Math. Phys.,12, No. 7, 500?505 (1986).

S. V. Kerov, A. N. Kirillov, and N. Yu. Reshetikhin, ?Combinatorics, Bethe Ansatz, and representations of the symmetric group? (this issue), 50?64.

L. A. Takhtadzhyan and L. D. Faddeev, ?Spectrum and scattering of stimuli in one-dimensional Heisenberg magnetics,? in: Differential Geometry Lie Groups and Mechanics. 4, J. Sov. Math.,24, No. 2 (1984).

H. Bethe, ?Zur Theorie der Metalle. I. Eigenwerte und Eigenfunktionen der linearen Atomkette,? Z. Physik,71, No. 3?4, 205?206 (1931).

C. Green, ?Some partitions associated with a partially ordered set,? J. Combin. Theory (A),20, 69?79 (1976).

C. Green and D. Kleitman, ?The structure of Sperner k-families,? J. Combin. Theor. (A),20, 41?68 (1976).

S. V. Fomin, ?Finite partially ordered sets and Young diagrams,? Dokl. Akad. Nauk SSSR,243, No. 5, 1144?1147 (1978).

D. Knuth, The Art of Computer Programming [Russian translation], Vol. 3, Moscow (1978).

A. V. Zelevenskii, ?Small resolutions of singularities of Schubert varieties,? Funkts. Anal. Prilozhen.,17, No. 2, 75?77 (1983).

W. J. Holman and L. C. Biedenharn, ?The representations and tensor operators of unitary groups,? in: Group Theory and Its Applications, Vol. II, E. M. Loebl (ed.), Academic Press, New York-London (1971).

R. Hotta and T. Springer, ?A specialization theorem for certain Weyl group representations and an application to the Green polynomials of unitary groups,? Inv. Math.,41, 113?127 (1977).

W. Borho and R. MacPherson, ?Representations of Weyl groups and intersection homology of nilpotent varieties,? C. R. Acad. Sci. Paris,292, 707?710 (1981).

L. D. Faddeev, ?Quantum completely integrable models of field theory,? in: Problems of Quantum Field Theory. Proceedings of the International Conference on Nonlocal Field Theory. Alushta, 1979 [in Russian], JINR (1979), pp. 249?299.

A. G. Izergin and V. E. Korepin, ?Problem of describing all L-operators for R-matrices of the XXX and XXZ models,? in: Questions of Quantum Field Theory and Statistical Physics, Vol. 4, J. Sov. Math.,30, No. 4 (1985).

V. G. Drinfel'd, ?Hopf algebras and the quantum Yang-Baxter equation,? Dokl. Akad. Nauk SSSR,283, No. 3, 1060?1064 (1985).

P. P. Kulish, N. Yu. Reshetikhin, and E. K. Sklyanin, ?Yang-Baxter equation and representation theory. I,? Lett. Math. Phys.,5, No. 5, 393?403 (1981).