Nilpotent Orbits in the Symplectic and Orthogonal Groups.
Abstract: Let K be an algebraically closed field of arbitrary characteristic
and consider a linear algebraic group G over K and its Lie algebra g. For X an element of
g, denote by O the orbit of X under the action of G on g defined by the adjoint
representation. The Zariski closure of O is then a subvariety of g. For G equal to either
the orthogonal or symplectic group, Kraft and Procesi showed ... read morethat the closure of O is a
normal variety for certain nilpotent elements X in g when the characteristic of K is equal
to 0. We begin to generalize their result for positive, odd characteristics, concluding
that the orbit closure of a nilpotent element X is normal if and only if it is normal in
the union of O with all orbits of codimension two contained in the boundary of the closure
of O. In particular, if the boundary of the closure of O does not contain any orbits of
codimension two, then O is normal.
Thesis (Ph.D.)--Tufts University, 2011.
Submitted to the Dept. of Mathematics.
Advisor: George McNinch.
Committee: Mark Reeder, Montserrat Teixidor i Bigas, and Richard Weiss.
Keyword: Mathematics.read less