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


Authors: L. Barchini and R. Zierau; with an appendix by Peter E. Trapa
Journal: Represent. Theory 12 (2008), 403-434
MSC (2000): Primary 20G20, 22E46
DOI: https://doi.org/10.1090/S1088-4165-08-00311-7
Published electronically: October 30, 2008
MathSciNet review: 2461236
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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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Additional Information

L. Barchini
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email: leticia@math.okstate.edu

R. Zierau
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email: zierau@math.okstate.edu

Peter E. Trapa
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email: ptrapa@math.utah.edu

DOI: https://doi.org/10.1090/S1088-4165-08-00311-7
Received by editor(s): April 5, 2008
Received by editor(s) in revised form: February 2, 2008
Published electronically: October 30, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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