This article is cited in 2 papers

Construction of invariants of the coadjoint representation of Lie groups using linear algebra methods

O. L. Kurnyavko^a, I. V. Shirokov<sup>ba

a</sup> Omsk Institute of Water Transport, Omsk, Russia
^b Omsk State Technical University, Omsk, Russia

Abstract: We offer a method for constructing invariants of the coadjoint representation of Lie groups that reduces this problem to known problems of linear algebra. This method is based on passing to symplectic coordinates on the coadjoint representation orbits, which play the role of local coordinates on those orbits. The corresponding transition functions are their parametric equations. Eliminating the symplectic coordinates from the transition functions, we can obtain the complete set of invariants. The proposed method allows solving the problem of constructing invariants of the coadjoint representation for Lie groups with an arbitrary dimension and structure.

Keywords: invariant, coadjoint representation, Lie group, Lie algebra, polarization, symplectic coordinate.

Received: 15.08.2015
Revised: 30.10.2015

DOI: 10.4213/tmf9025

 English version: Theoretical and Mathematical Physics, 2016, 188:1, 965–979

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