| Abstract: | Suppose G is a connected reductive algebraic group, P is a parabolic subgroup of G, L is a Levi factor of P, and e is a regular nilpotent element in Lie L. We assume that the characteristic of the underlying field is good for G. Choose a maximal torus, T, and a Borel subgroup, B, of G, so that T?B∩L, B ? P and e ∈ Lie B. Let β be the variety of Borel subgroups of G and let ??e be the subset of ?? consisting of Borel subgroups whose Lie algebras contain e. Finally, let W be the Weyl group of G with respect to T. For ω ∈ W let ??ω be the B-orbit in ?? containing ωB. We consider the intersections ??ω ∩ ??e. The main result is that if dim ??ω ∩ ??e = dim ??e, then ??ω ∩ ??e is an affine space. Thus, the irreducible components of ??e are indexed by Weyl group elements. It is also shown that if G is of type A, then this set of Weyl group elements is a right cell in W. |
