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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 − λiI)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.
Original language | English |
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Pages (from-to) | 651-661 |
Number of pages | 11 |
Journal | Journal of Mathematical Sciences (United States) |
Volume | 213 |
Issue number | 5 |
Early online date | 9 Feb 2016 |
DOIs | |
State | Published - 2016 |
ID: 35280104