### 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 |