Lax formalism for Gelfand-Tsetlin integrable systems

Author(s)

Correa, Eder M. ^[1] ; Grama, Lino ^[2]

Affiliation

^[1] Univ Fed Minas Gerais, Ave Antonio Carlos 6627, BR-31270901 Belo Horizonte, MG - Brazil

^[2] Imecc Unicamp, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: BULLETIN DES SCIENCES MATHEMATIQUES; v. 170, SEP 2021.
• Web of Science Citations: 0

Abstract

In the present work, we study Hamiltonian systems on (co)adjoint orbits and propose a Lax pair formalism for Gelfand-Tsetlin integrable systems defined on (co)adjoint orbits of the compact Lie groups U(n) and SO(n). In the particular setting of (co)adjoint orbits of U(n), by means of the associated Lax matrix we construct a family of algebraic curves which encodes the Gelfand-Tsetlin integrable systems as branch points. This family of algebraic curves enables us to explore some new insights into the relationship between the topology of singular Gelfand-Tsetlin fibers, singular algebraic curves and vanishing cycles. Further, we provide a new description for Guillemin and Sternberg's action coordinates in terms of hyperelliptic integrals. (C) 2021 Elsevier Masson SAS. All rights reserved. (AU)

• FAPESP's process: 18/13481-0 - Geometry of control, dynamical and stochastic systems
• Grantee: Marco Antônio Teixeira
• Support Opportunities: Research Projects - Thematic Grants