Bulg. J. Phys. vol.35 no.s1 (2008), pp. 352-363

Gelfand-Tsetlin Bases for Representations of Finite W-Algebras and Shifted Yangians

V. Futorny1, A. Molev2, S. Ovsienko3
1Institute of Mathematics and Statistics, University of São Paulo, Caixa Postal 66281- CEP 05315-970, São Paulo, Brazil
2School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
3Faculty of Mechanics and Mathematics, Kiev Taras Shevchenko University, Vladimirskaya 64, 00133, Kiev, Ukraine
Abstract. Remarkable subalgebras of the Yangian for gln called the shifted Yangians were introduced in a recent work by Brundan and Kleshchev in relation to their study of finite W-algebras. In particular, in that work a classification of finite-dimensional irreducible representations of the shifted Yangians and the associated finite W-algebras was given. We construct a class of these representations in an explicit form via bases of Gelfand-Tsetlin type.

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