Nilpotent orbits and finite W-algebras

Abstract

In recent years, the finite W-algebras associated to a semisimple Lie algebra and its nilpotent element have been studied intensively from different viewpoints. In this lecture series, we shall present some basic constructions, connections, and applications of finite W-algebras.

40 pages, lectures for Ottawa summer school 2009, v2, references added and updated, Introduction clarified, other minor changes.

References in corpus (4)

• On the structure of the category O for W-algebras
• Harish-Chandra bimodules for quantized Slodowy slices
• Singular blocks of parabolic category O and finite W-algebras
• Representations of Lie superalgebras in prime characteristic II: The queer series

Cited by in corpus (12)

• Finite W-superalgebras via super Yangians
• Galilean contractions of $W$-algebras
• On shifted super Yangians and a class of finite W-superalgebras
• On the finite $W$-algebra for the Lie superalgebra Q(N) in the non-regular case
• Quantizations of regular functions on nilpotent orbits
• W-algebras and Whittaker categories
• Minimal W-superalgebras and modular representations of basic Lie superalgebras
• C_2-cofinite W-algebras and their logarithmic representations
• Quantum Hamiltonian reduction of W-algebras and category O
• On integrability of transverse Lie-Poisson structures at nilpotent elements
• On Kostant's theorem for the Lie superalgebra Q(n)
• Injectivity of a certain cycle map for finite dimensional W-algebras