Candidate: Joseph A. Fox

Degree of: Doctor of Philosophy

Department: Mathematics

Title: Nilpotent Orbits on Infinitesimal Symmetric Spaces

Committee: Dr. Terrell L. Hodge, Chair
Dr. John Martino
Dr. Annegret Paul
Dr. Brian Parshall
Dr. Jay Wood

Date: Friday, March 17, 2006 2:00 p.m.- 5:00 p.m.
Alavi Commons Room (Everett 6625)

Abstract: Let G be a reductive linear algebraic group defined over an algebraically closed field k whose characteristic is good for G. Let be an involution defined on G, and let K be the subgroup of G consisting of elements fixed by . The differential of , also denoted , is an involution of the Lie algebra g = Lie (G), and it decomposes g into +1- and -1-eigenspaces, k and p, respectively. The space p identifies with the tangent space at the identity of the symmetric space G / K. In this dissertation, we are interested in the adjoint action of K on p, or more specifically, on the nullcone N (p), which consists of the nilpotent elements of p. The main result is a new classification of the K-orbits on N (p).

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