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

Barchini, L.; Zierau, R.

doi:10.1090/S1088-4165-08-00311-7

Certain components of Springer fibers and associated cycles for discrete series representations of $SU(p,q)$
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by L. Barchini and R. Zierau; \\with an appendix by Peter E. Trapa

Represent. Theory 12 (2008), 403-434

DOI: https://doi.org/10.1090/S1088-4165-08-00311-7

Published electronically: October 30, 2008

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Abstract:

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 $S(GL(p)\times GL(q))$-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.

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