Quantum Integrability and Generalised Quantum Schubert Calculus
Representation Theory
2017-05-24 v4 Algebraic Geometry
K-Theory and Homology
Quantum Algebra
Exactly Solvable and Integrable Systems
Abstract
We introduce and study a new mathematical structure in the generalised (quantum) cohomology theory for Grassmannians. Namely, we relate the Schubert calculus to a quantum integrable system known in the physics literature as the asymmetric six-vertex model. Our approach offers a new perspective on already established and well-studied special cases, for example equivariant K-theory, and in addition allows us to formulate a conjecture on the so-far unknown case of quantum equivariant K-theory.
Cite
@article{arxiv.1408.4718,
title = {Quantum Integrability and Generalised Quantum Schubert Calculus},
author = {Vassily Gorbounov and Christian Korff},
journal= {arXiv preprint arXiv:1408.4718},
year = {2017}
}
Comments
57 pages, 10 figures; v2: some references added and some minor changes; v3: abstract shortened, some typos corrected and a discussion of the Bethe roots for the non-equivariant case added; v4: accepted version