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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Classification of problematic subgroups of $ \boldsymbol{U(n)}$


Authors: Julia E. Bergner, Ruth Joachimi, Kathryn Lesh, Vesna Stojanoska and Kirsten Wickelgren
Journal: Trans. Amer. Math. Soc. 371 (2019), 6739-6777
MSC (2010): Primary 55N91; Secondary 55P65, 55R45
DOI: https://doi.org/10.1090/tran/7442
Published electronically: February 20, 2019
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Abstract: Let $ \mathcal {L}_n$ denote the topological poset of decompositions of $ \mathbb{C}^n$ into mutually orthogonal subspaces. We classify $ p$-toral subgroups of $ U(n)$ that can have noncontractible fixed points under the action of $ U(n)$ on  $ \mathcal {L}_n$.


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Additional Information

Julia E. Bergner
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia
Email: bergnerj@member.ams.org

Ruth Joachimi
Affiliation: Department of Mathematics and Informatics, University of Wuppertal, Wuppertal, Germany
Email: joachimi@math.uni-wuppertal.de

Kathryn Lesh
Affiliation: Department of Mathematics, Union College, Schenectady, New York
Email: leshk@union.edu

Vesna Stojanoska
Affiliation: Department of Mathematics, University of Illinois at Urbana–Champaign, Urbana, Illinois
Email: vesna@illinois.edu

Kirsten Wickelgren
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia
Email: kwickelgren3@math.gatech.edu

DOI: https://doi.org/10.1090/tran/7442
Received by editor(s): September 4, 2014
Received by editor(s) in revised form: February 2, 2017, and August 25, 2017
Published electronically: February 20, 2019
Additional Notes: The first author received partial support from NSF grants DMS-1105766 and DMS-1352298. Some of this work was done while she was in residence at MSRI during the Spring 2014 semester, supported by NSF grant 0932078 000.
The second author was partially supported by DFG grant HO 4729/1-1.
The third author received partial support from NSF grant DMS-0968251.
The fourth author received partial support from NSF grants DMS-1307390 and DMS-160647. Some of this work was done while she was in residence at MSRI during the Spring 2014 semester, supported by NSF grant 0932078 000.
The fifth author was partially supported by an AIM five-year fellowship and by NSF grants DMS-1406380 and DMS-1552730. Some of this work was done while she was in residence at MSRI during the Spring 2014 semester, supported by NSF grant 0932078 000.
The authors thank the Banff International Research Station and the Clay Mathematics Institute for the financial support.
Article copyright: © Copyright 2019 American Mathematical Society