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 language | English |
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Pages (from-to) | 1880-1925 |
Number of pages | 46 |
Journal | International Mathematics Research Notices |
Volume | 2011 |
Issue number | 8 |
Early online date | 19 Jul 2010 |
DOIs | |
Publication status | Published - 2011 |