Components of Springer fibers for the exceptional groups G2 and F4

Let G be the complex connected simply connected simple Lie group of type G(2) or F-4. Let K denote the fixed point subgroup relative to an involution of G that is lifted from a Cartan involution. This article gives a description of certain components of Springer fibers associated to closed K-orbits contained in the flag variety of G. These components allow us to describe certain multiplicity polynomials associated to discrete series representations of the real form G(2)(2) of G2 and the two real forms F-4(4) and F-4(-20) of F-4. The goals for this paper are motivated by the descriptions of Springer fiber components and the associated multiplicity polynomials for type SU(p, q) described in a paper of Barchini and Zierau. (C) 2013 Elsevier Inc. All rights reserved.