Book Review

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MathSciNet review: 2651087

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Book Information:

Author: Alexander Molev

Title: Yangians and classical Lie algebras

Additional book information: Mathematical Surveys and Monographs, 143, American Mathematical Society, Providence, RI, 2007, xviii+400 pp., ISBN 13: 978-0-8218-4374-1, US$99 hardcover

*Drinfeld functor and finite-dimensional representations of Yangian*, Comm. Math. Phys.

**205**(1999), no. 1, 1–18. MR

**1706920**, DOI 10.1007/s002200050664

*Twisted Yangians and finite $W$-algebras*, Transform. Groups

**14**(2009), no. 1, 87–114. MR

**2480853**, DOI 10.1007/s00031-008-9041-x

*Shifted Yangians and finite $W$-algebras*, Adv. Math.

**200**(2006), no. 1, 136–195. MR

**2199632**, DOI 10.1016/j.aim.2004.11.004

*A new interpretation of Gel′fand-Tzetlin bases*, Duke Math. J.

**54**(1987), no. 2, 563–577. MR

**899405**, DOI 10.1215/S0012-7094-87-05423-8

*Algèbres enveloppantes*, Cahiers Scientifiques, Fasc. XXXVII, Gauthier-Villars Éditeur, Paris-Brussels-Montreal, Que., 1974 (French). MR

**0498737**

*Hopf algebras and the quantum Yang-Baxter equation*, Dokl. Akad. Nauk SSSR

**283**(1985), no. 5, 1060–1064 (Russian). MR

**802128**

*Degenerate affine Hecke algebras and Yangians*, Funktsional. Anal. i Prilozhen.

**20**(1986), no. 1, 69–70 (Russian). MR

**831053**

*Quantum groups*, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 798–820. MR

**934283**

*A new realization of Yangians and of quantum affine algebras*, Dokl. Akad. Nauk SSSR

**296**(1987), no. 1, 13–17 (Russian); English transl., Soviet Math. Dokl.

**36**(1988), no. 2, 212–216. MR

**914215**

*Finite-dimensional representations of the group of unimodular matrices*, Doklady Akad. Nauk SSSR (N.S.)

**71**(1950), 825–828 (Russian). MR

**0035774**

*Finite-dimensional irreducible representations of twisted Yangians*, J. Math. Phys.

**39**(1998), no. 10, 5559–5600. MR

**1642338**, DOI 10.1063/1.532551

*Yangians and classical Lie algebras*, Uspekhi Mat. Nauk

**51**(1996), no. 2(308), 27–104 (Russian); English transl., Russian Math. Surveys

**51**(1996), no. 2, 205–282. MR

**1401535**, DOI 10.1070/RM1996v051n02ABEH002772

*Representations of Yangians with Gelfand-Zetlin bases*, J. Reine Angew. Math.

**496**(1998), 181–212. MR

**1605817**, DOI 10.1515/crll.1998.029

*Twisted Yangians and infinite-dimensional classical Lie algebras*, Quantum groups (Leningrad, 1990) Lecture Notes in Math., vol. 1510, Springer, Berlin, 1992, pp. 104–119. MR

**1183482**, DOI 10.1007/BFb0101183

*Quantization of Lie groups and Lie algebras*, Algebra i Analiz

**1**(1989), no. 1, 178–206 (Russian); English transl., Leningrad Math. J.

**1**(1990), no. 1, 193–225. MR

**1015339**

*The classical groups*, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Their invariants and representations; Fifteenth printing; Princeton Paperbacks. MR

**1488158**

Review Information:

Reviewer: Jonathan Brundan

Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403

Email: brundan@uoregon.edu

Journal: Bull. Amer. Math. Soc.

**47**(2010), 561-566

DOI: https://doi.org/10.1090/S0273-0979-10-01280-2

Published electronically: February 9, 2010

Additional Notes: The reviewer was supported in part by NSF Grant DMS-0635607.

Review copyright: © Copyright 2010 American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.