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Zap. Nauchn. Sem. POMI, 2015, Volume 433, Pages 41–64 (Mi znsl6126)  

This article is cited in 2 scientific papers (total in 2 papers)

Young tableaux and stratification of space of complex square matrices

M. V. Babichab

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia

Abstract: A stratification of the manifold of all square matrices is considered. One equivalence class consists of the matrices with the same sets of non-vanishing values $\mathrm{rank}(A-\lambda_i\mathrm I)^j$. The stratification is consistent with a fibration on the submanifolds of matrices similar to each other, i.e. with the adjoint orbits fibration. Internal structures of the matrices from one equivalence class are very similar, among other factors their (co)adjoint orbits are canonically birationally symplectomorphic. A Young tableaux technic developed in the article describes this stratification and the fibration of the strata on the (co)adjoint orbits.

Key words and phrases: Young tableau, Jordan type, invariant subspace, stratification, space of square matrices.

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English version:
Journal of Mathematical Sciences (New York), 2016, 213:5, 651–661

Bibliographic databases:

UDC: 517.9
Received: 11.03.2015

Citation: M. V. Babich, “Young tableaux and stratification of space of complex square matrices”, Questions of quantum field theory and statistical physics. Part 23, Zap. Nauchn. Sem. POMI, 433, POMI, St. Petersburg, 2015, 41–64; J. Math. Sci. (N. Y.), 213:5 (2016), 651–661

Citation in format AMSBIB
\Bibitem{Bab15}
\by M.~V.~Babich
\paper Young tableaux and stratification of space of complex square matrices
\inbook Questions of quantum field theory and statistical physics. Part~23
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 433
\pages 41--64
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6126}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3493679}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 213
\issue 5
\pages 651--661
\crossref{https://doi.org/10.1007/s10958-016-2729-x}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84957614047}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. V. Babich, “Birational Darboux coordinates on nilpotent coadjoint orbits classical complex Lie groups, Jordan blocks $2\times2$”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 24, Zap. nauchn. sem. POMI, 465, POMI, SPb., 2017, 5–12  mathnet
    2. M. V. Babich, “On parametrization of symplectic quotient of Cartesian product of coadjoint orbits of complex general linear group with respect to its diagonal action”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 25, K 70-letiyu M. A. Semenova-Tyan-Shanskogo, Zap. nauchn. sem. POMI, 473, POMI, SPb., 2018, 7–16  mathnet
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