TY - JOUR
T1 - Lusztig Factorization Dynamics of the Full Kostant–Toda Lattices
AU - Ercolani, Nicholas M.
AU - Ramalheira-Tsu, Jonathan
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature B.V.
PY - 2023/3
Y1 - 2023/3
N2 - 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 the Full Kostant–Toda Lattice that does not involve any capacities or colorings, and which has a natural interpretation in terms of the Robinson–Schensted–Knuth algorithm. We provide as well an extension of O’Connell’s ordinary differential equations to the Full Kostant–Toda Lattice.
AB - 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 the Full Kostant–Toda Lattice that does not involve any capacities or colorings, and which has a natural interpretation in terms of the Robinson–Schensted–Knuth algorithm. We provide as well an extension of O’Connell’s ordinary differential equations to the Full Kostant–Toda Lattice.
KW - Box–ball system
KW - Integrability
KW - Lusztig factorization
KW - Toda lattice
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U2 - 10.1007/s11040-022-09444-3
DO - 10.1007/s11040-022-09444-3
M3 - Article
AN - SCOPUS:85146319157
SN - 1385-0172
VL - 26
JO - Mathematical Physics Analysis and Geometry
JF - Mathematical Physics Analysis and Geometry
IS - 1
M1 - 2
ER -