### Abstract

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 |

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**Algebraic Group Analogues of the Slodowy Slices and Deformations of Poisson W-algebras.** / Sevastyanov, Alexey.

Research output: Contribution to journal › Article

*International Mathematics Research Notices*, vol. 2011, no. 8, pp. 1880-1925. https://doi.org/10.1093/imrn/rnq139

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TY - JOUR

T1 - Algebraic Group Analogues of the Slodowy Slices and Deformations of Poisson W-algebras

AU - Sevastyanov, Alexey

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

U2 - 10.1093/imrn/rnq139

DO - 10.1093/imrn/rnq139

M3 - Article

VL - 2011

SP - 1880

EP - 1925

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 8

ER -