Date of Award


Degree Name

Doctor of Philosophy




Let G be a reductive linear algebraic group defined over an algebraically closed field k whose characteristic is good for G. Let [straight theta] be an involution defined on G, and let K be the subgroup of G consisting of elements fixed by [straight theta]. The differential of [straight theta], also denoted [straight theta], is an involution of the Lie algebra [Special characters omitted.] = Lie (G ), and it decomposes [Special characters omitted.] into +1- and -1-eigenspaces, [Special characters omitted.] and [Special characters omitted.] , respectively. The space [Special characters omitted.] 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 [Special characters omitted.] , or more specifically, on the nullcone [Special characters omitted.] , which consists of the nilpotent elements of [Special characters omitted.] . The main result is a new classification of the K -orbits on [Special characters omitted.] .

*Full abstract attached.

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Dissertation-Open Access

2006_Fox_J_Abstract.pdf (53 kB)

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Mathematics Commons