Integrable systems associated with the Bruhat Poisson structures

2001/02/26 by Philip Foth, Foth, Philip
Mathematics · Physics and Astronomy · #53B35 #53C35 #58F07 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Waves and Solitons #math.DG #math.DS #msc:53B35 #msc:53C35 #msc:58F07

paper · pdf · doi:10.48550/arxiv.math/0102192

replaced with an enhanced version

openalex publication_date 2001/02/26 · arxiv created 2001/06/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this note is to give a simple description of a (complete) family of functions in involution on certain hermitian symmetric spaces. This family, obtained via bi-hamiltonian approach using the Bruhat Poisson structure, is especially simple for the projective spaces, where the formulas in terms of the moment map coordinates are presented. We show how these functions are related to the Gelfand-Tsetlin coordinates. We also show how the Lenard scheme can be applied.

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