Algebraic Group Analogues of the Slodowy Slices and Deformations of Poisson W-algebras

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Abstract

We define algebraic group analogues of the Slodowy transversal slices to adjoint orbits in a complex semisimple Lie algebra Graphic. The new slices are transversal to the conjugacy classes in an algebraic group G with Lie algebra g. These slices are associated to (the conjugacy classes of) elements s of the Weyl group W of g. For such slices, we prove an analogue of the Kostant cross-section theorem for the action of a unipotent group. Using this theorem, we equip the new slices with certain Poisson structures obtained by Poisson reduction from a Poisson–Lie group structure on G.
Original languageEnglish
Pages (from-to)1880-1925
Number of pages46
JournalInternational Mathematics Research Notices
Volume2011
Issue number8
Early online date19 Jul 2010
DOIs
Publication statusPublished - 2011

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