Journal of Mathematical Sciences

, Volume 238, Issue 6, pp 763–768 | Cite as

Birational Darboux Coordinates on Nilpotent Coadjoint Orbits of Classical Complex Lie Groups, the Case of 2 × 2 Jordan Blocks

  • M. V. BabichEmail author

We consider the problem of constructing birational Darboux coordinates on nilpotent coadjoint orbits of the complex Lie groups SO(N, ℂ) and Sp(N, ℂ). The nilpotent case is the most difficult one. Difficulties arise if the Jordan form of matrices from the orbit under consideration contains Jordan blocks of sizes of different parity. The desired coordinates have been found on orbits consisting of matrices with 1 × 1 and 2 × 2 Jordan blocks. Explicit formulas for them are given in the paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Institute of MathematicsSt. Petersburg State UniversitySt. PetersburgRussia

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