Lusztig Factorization Dynamics of the Full Kostant-Toda Lattices
Abstract
We study extensions of the classical Toda lattices at several different space-time scales. These extensions are from the classical tridiagonal phase spaces to the phase space of full Hessenberg matrices, referred to as the Full Kostant-Toda Lattice. Our formulation makes it natural to make further Lie-theoretic generalizations to dual spaces of Borel Lie algebras. Our study brings into play factorizations of Loewner-Whitney type in terms of canonical coordinatizations due to Lusztig. Using these coordinates we formulate precise conditions for the well-posedness of the dynamics at the different space-time scales. Along the way we derive a novel, minimal box-ball system for Full Toda that doesn't involve any capacities or colorings, as well as an extension of O'Connell's ODEs to Full Toda.
Keywords
Cite
@article{arxiv.2203.15164,
title = {Lusztig Factorization Dynamics of the Full Kostant-Toda Lattices},
author = {Nicholas M. Ercolani and Jonathan Ramalheira-Tsu},
journal= {arXiv preprint arXiv:2203.15164},
year = {2023}
}