Local Systems on Nilpotent Orbits and Weighted Dynkin Diagrams

2002/01/25 by Pramod N. Achar, Pramod Achar, Eric Sommers +2
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.math/0201248

11 pages

arxiv created 2002/01/25 · openalex publication_date 2002/01/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Lusztig-Vogan bijection for the case of a local system. We compute the bijection explicitly in type A for a local system and then show that the dominant weights obtained for different local systems on the same orbit are related in a manner made precise in the paper. We also give a conjecture (putatively valid for all groups) detailing how the weighted Dynkin diagram for a nilpotent orbit in the dual Lie algebra should arise under the bijection.

Citations

• On the equivariant K-theory of the nilpotent cone

Related

• Weighted Vogan diagrams associated to real nilpotent orbits
• Local Systems on Classical Nilpotent Orbits and Maximal Length Elements
• Some Calculations of the Lusztig-Vogan Bijection for Classical Nilpotent Orbits
• On divisible weighted Dynkin diagrams and reachable elements
• Irreducible local systems on nilpotent orbits