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Yangians and universal enveloping algebras. (English. Russian original) Zbl 0691.17005

J. Sov. Math. 47, No. 2, 2466-2473 (1989); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 164, 142-150 (1987).
See the review in Zbl 0668.17009.

MSC:

17B35 Universal enveloping (super)algebras
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B65 Infinite-dimensional Lie (super)algebras

Citations:

Zbl 0668.17009
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References:

[1] J. Dixmier, Universal Enveloping Algebras [Russian translation], Moscow (1978).
[2] V. G. Drinfel’d, ”Quantum groups,” J. Sov. Math.,41, No. 2 (1988).
[3] V. G. Kac, ”Laplace operators of infinite-dimensional Lie algebras and theta functions,” Proc. Nat. Acad. Sci. USA,81, 645–647 (1984). · Zbl 0532.17008 · doi:10.1073/pnas.81.2.645
[4] P. P. Kulish and E. K. Sklyanin, ”Quantum spectral transform. Recent developments,” Lect. Notes Physics,151, 61–119 (1982). · Zbl 0734.35071 · doi:10.1007/3-540-11190-5_8
[5] I. MacDonald, Symmetric Functions and Hall Polynomials [Russian translation], Moscow (1985). · Zbl 0672.20007
[6] G. I. Ol’shanskii, ”Unitary representations of infinite-dimensional classical groups U ({\(\rho\)},, S00({\(\rho\)},, S{\(\rho\)}({\(\rho\)}, and the corresponding groups of motions,” Funkts. Anal. Prilozhen.,12, No. 3, 32–44 (1978).
[7] G. I. Ol’shanskii, ”Infinite-dimensional classical groups of finite \(\mathbb{R}\) -rank: description of representations and asymptotic theory,” Funkts. Anal. Prilozhen.,18, No. 1, 28–42 (1984).
[8] L. A. Takhtadzhyan and L. D. Faddeev, ”Quantum method of the inverse problem and the XYZ Heisenberg model,” Usp. Mat. Nauk,34, No. 5, 13–63 (1979).
[9] I. V. Cherednik, ”q-analogs of Gel’fand-Tsetlin bases,” Preprint Inst. Teor. Éksp. Fiz. (ITÉF), Moscow (1986). · Zbl 0645.17007
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