The relativistic Toda Lattice and quantum K-Schubert classes of the flag variety
APA
(2024). The relativistic Toda Lattice and quantum K-Schubert classes of the flag variety. SciVideos. https://youtube.com/live/czCz0ssibBo
MLA
The relativistic Toda Lattice and quantum K-Schubert classes of the flag variety. SciVideos, Nov. 01, 2024, https://youtube.com/live/czCz0ssibBo
BibTex
@misc{ scivideos_ICTS:30056,
doi = {},
url = {https://youtube.com/live/czCz0ssibBo},
author = {},
keywords = {},
language = {en},
title = {The relativistic Toda Lattice and quantum K-Schubert classes of the flag variety},
publisher = {},
year = {2024},
month = {nov},
note = {ICTS:30056 see, \url{https://scivideos.org/icts-tifr/30056}}
}
Abstract
The quantum K-theory of the flag variety is a ring defined by introducing a quantum product to the K-theory of the flag variety. Under appropriate localization, it is known that the following three rings (i), (ii), and (iii) are isomorphic, and this property allows for a detailed investigation of each ring: (i)the coordinate ring of the phase space of the relativistic Toda lattice, (ii) the quantum equivariant K-theory of the flag variety, and (iii) the K-equivariant homology ring of the affine Grassmannian.
The isomorphism between (i) and (ii) is derived from the Lax formalism of the relativistic Toda lattice [Ikeda-Iwao-Maeno]. The isomorphism between (ii) and (iii) is referred to as the K-Peterson isomorphism [Lam-Li-Mihalcea-Shimozono, Kato, Chow-Leung, Ikeda-Iwao-Maeno]. In this talk, I will outline how techniques from classical integrable systems, such as the construction of algebraic solutions and Bäcklund transformations, are applied to the study of geometry. This talk is ba...