A stratification of the manifold of all square matrices is considered. One equivalence class consists of the matrices with the same sets of values of rank(A − λi I)j . The stratification is consistent with a fibration on submanifolds of matrices similar to each other, i.e., with the adjoint orbits fibration. Internal structures of matrices from one equivalence class are very similar; among other factors, their (co)adjoint orbits are birationally symplectomorphic. The Young tableaux technique developed in the paper describes this stratification and the fibration of the strata on (co)adjoint orbits.
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To Petr Petrovich Kulish on the occasion of his 70th anniversary
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 433, 2015, pp. 41–64.
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Babich, M.V. Young Tableaux and Stratification of the Space of Square Complex Matrices. J Math Sci 213, 651–661 (2016). https://doi.org/10.1007/s10958-016-2729-x
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DOI: https://doi.org/10.1007/s10958-016-2729-x