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

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