2021
Correa, Eder M.; Grama, Lino
Lax formalism for Gelfand-Tsetlin integrable systems Journal Article
Em: Bulletin des Sciences Mathématiques, vol. 170, 2021.
Resumo | Links | BibTeX | Tags: Gelfand-Tsetlin
@article{nokey,
title = {Lax formalism for Gelfand-Tsetlin integrable systems},
author = {Eder M. Correa and Lino Grama},
url = {https://www.sciencedirect.com/science/article/abs/pii/S0007449721000555?via%3Dihub},
doi = {https://doi.org/10.1016/j.bulsci.2021.102999},
year = {2021},
date = {2021-05-25},
journal = {Bulletin des Sciences Math\'{e}matiques},
volume = {170},
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 and . In the particular setting of (co)adjoint orbits of , 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.},
keywords = {Gelfand-Tsetlin},
pubstate = {published},
tppubtype = {article}
}
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 and . In the particular setting of (co)adjoint orbits of , 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.