The structure of the nilpotent cone, the Kazhdan-Lusztig map and algebraic group analogues of the Slodowy slices

2008/09/01 by A. Sevostyanov, Sevostyanov, A. · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0809.0205

Abstract

We define algebraic group analogues of the Slodowy transversal slices to adjoint orbits in a complex semisimple Lie algebra g. 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.

Cited by

• Root systems and diagram calculus. I. Regular extensions of Carter diagrams and the uniqueness of conjugacy classes
• The Poisson geometry of the conjugation quotient map for simple algebraic groups and deformed Poisson W-algebras

Related

• From braids to transverse slices in reductive groups
• Strictly transversal slices to conjugacy classes in algebraic groups
• Conjugacy classes in Weyl groups and q-W algebras
• Automorphism sheaves, spectral covers, and the Kostant and Steinberg sections
• Local geometry of special pieces of nilpotent orbits