The Poisson geometry of the conjugation quotient map for simple algebraic groups and deformed Poisson W-algebras

Details The Poisson geometry of the conjugation quotient map for simple algebraic groups and deformed Poisson W-algebras The Poisson geometry of the conjugation quotient map for simple algebraic groups and deformed Poisson W-algebras

2009-01-29

arxiv.org/abs/0901.4746v3

Mathematics

Representation Theory

24 pages, LaTeX 2e

Scientific paper

We define Poisson structures on certain transversal slices to conjugacy classes in complex simple algebraic groups introduced in arXiv:0809.0205. These slices are associated to the elements of the Weyl group, and the Poisson structures on them are analogous to the Poisson structures introduced by J. de Boer, T. Tjin and A. Premet in papers arXiv:hep-th/9211109 and http://www.maths.man.ac.uk/DeptWeb/Homepages/aap/Reprints/Transverse.ps on the Slodowy slices in complex simple Lie algebras. The quantum deformations of these Poisson structures are known as W-algebras of finite type. As an application of our definition we obtain some new Poisson structures on the coordinate rings of simple Kleinian singularities.

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