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

作者：Sevostyanov Alexey^*

来源：International Mathematics Research Notices, 2011, (8): 1880-1925.

DOI：10.1093/imrn/rnq139

We define algebraic group analogues of the Slodowy transversal slices to adjoint orbits in a complex semisimple Lie algebra . The new slices are transversal to the conjugacy classes in an algebraic group G with Lie algebra . These slices are associated to (the conjugacy classes of) elements s of the Weyl group W of . 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.

• 出版日期2011