Local Systems on Classical Nilpotent Orbits and Maximal Length Elements

2013/08/09 by Wong, Kayue Daniel
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1308.2020

Abstract

It is known that there is a bijection between dominant weights of a complex reductive Lie group G and the set N_O,r whose elements are of the form (O,ρ), where O is a nilpotent orbit and ρ is an irreducible, algebraic representation of the stabilizer group G^e of an element e in the nilpotent orbit O. We would like to study the above bijection when G is classical and ρ corresponds to a local system of O. In particular, we will prove Conjecture 3.1 in \citeAS and Conjecture 7.4' in \citeAc2 in the classical setting.

Related

• Irreducible local systems on nilpotent orbits
• Local Systems on Nilpotent Orbits and Weighted Dynkin Diagrams
• Flags and orbits of connected reductive groups over local rings
• K-orbits on the flag variety and strongly regular nilpotent matrices
• General Linear and Symplectic Nilpotent Orbit Varieties