Representations of shifted Yangians and finite W-algebras

Details Representations of shifted Yangians and finite W-algebras Representations of shifted Yangians and finite W-algebras

2005-07-30

arxiv.org/abs/math/0508003v3

Mem. Amer. Math. Soc. 196 (2008), 107 pp.

Mathematics

Representation Theory

109 pages; v3: substantial changes to treatment of Whittaker functor in chapter 8, minor related changes elsewhere including m

Scientific paper

We study highest weight representations of shifted Yangians over an algebraically closed field of characteristic 0. In particular, we classify the finite dimensional irreducible representations and explain how to compute their Gelfand-Tsetlin characters in terms of known characters of standard modules and certain Kazhdan-Lusztig polynomials. Our approach exploits the relationship between shifted Yangians and the finite W-algebras associated to nilpotent orbits in general linear Lie algebras.

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