Certain components of Springer fibers and associated cycles for discrete series representations of 𝑆𝑈(𝑝,𝑞)

Abstract

An explicit geometric description of certain components of Springer fibers for S L ( n , C ) SL(n,C) s given in this article. These components are associated to closed S ( G L ( p ) × G L ( q ) ) S(GL(p)\times GL(q)) -orbits in the flag variety. The geometric results are used to compute the associated cycles of the discrete series representations of S U ( p , q ) SU(p,q) . A discussion of an alternative, and more general, computation of associated cycles is given in the appendix.