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Operations on arc diagrams and degenerations for invariant subspaces of linear operators


Authors: Justyna Kosakowska and Markus Schmidmeier
Journal: Trans. Amer. Math. Soc. 367 (2015), 5475-5505
MSC (2010): Primary 14L30, 16G20; Secondary 16G70, 05C85, 47A15
DOI: https://doi.org/10.1090/S0002-9947-2014-06206-5
Published electronically: December 24, 2014
MathSciNet review: 3347180
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Abstract: We study geometric properties of varieties associated with invariant subspaces of nilpotent operators. There are algebraic groups acting on these varieties, and we give dimensions of orbits of these actions. Moreover, a combinatorial characterization of the partial order given by degenerations is described.


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Additional Information

Justyna Kosakowska
Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland
Email: justus@mat.umk.pl

Markus Schmidmeier
Affiliation: Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, Florida 33431
Email: markus@math.fau.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06206-5
Keywords: Degenerations, partial orders, Hall polynomials, nilpotent operators, invariant subspaces, Littlewood-Richardson tableaux
Received by editor(s): February 13, 2012
Received by editor(s) in revised form: August 16, 2012, and June 4, 2013
Published electronically: December 24, 2014
Additional Notes: The first named author was partially supported by Research Grant No. DEC-2011/02/A/ST1/00216 of the Polish National Science Center
Dedicated: Dedicated to Professor Daniel Simson on the occasion of his 70th birthday
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.