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Finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent orbits in classical Lie algebras

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Abstract

We consider finite W-algebras \({U(\mathfrak{g},e)}\) associated to even multiplicity nilpotent elements in classical Lie algebras. We give a classification of finite dimensional irreducible \({U(\mathfrak{g},e)}\)-modules with integral central character in terms of the highest weight theory from Brundan et al. (Int. Math. Res. Notices 15, art. ID rnn051, 2008). As a corollary, we obtain a parametrization of primitive ideals of \({U(\mathfrak{g})}\) with associated variety the closure of the adjoint orbit of e and integral central character.

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  1. School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK

    Jonathan S. Brown & Simon M. Goodwin

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  1. Jonathan S. Brown
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  2. Simon M. Goodwin
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Correspondence to Simon M. Goodwin.

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Brown, J.S., Goodwin, S.M. Finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent orbits in classical Lie algebras. Math. Z. 273, 123–160 (2013). https://doi.org/10.1007/s00209-012-0998-8

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