Quantum Difference Equations for Grassmannians

2025/10/24 by Cheng, Xingyu, Lance, Reese, Nagabandi, Nikhil +1
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2510.21653

Abstract

We consider quantum difference equation (QDE) for equivariant quantum K-theory of the Grassmannian. In this paper we obtain a solution to the QDE and use the solution to asymptotically derive the Bethe ansatz equations. In the limit, we obtain similar results for the cohomological analogue. For both cases, we describe the nonequivariant solutions as well. As an application, we identify the quantum K-theory ring of Gr(k,n) with a quantum 5 vertex XXZ integrable spin chain.

Citations

• On the Satake correspondence for the equivariant quantum differential equations and qKZ difference equations of Grassmannians
• On Seidel representation in quantum K-theory of Grassmannians
• Free Fermion Six Vertex Model: Symmetric Functions and Random Domino Tilings
• Quasimap counts and Bethe eigenfunctions
• Littlewood-Richardson coefficients for Grothendieck polynomials from integrability
• Quantum difference equation for Nakajima varieties
• On the WDVV-equation in quantum K-theory

Related

• Quantum K-theory and q-Difference equations
• On the Satake correspondence for the equivariant quantum differential equations and qKZ difference equations of Grassmannians
• A correspondence between the quantum K theory and quantum cohomology of Grassmannians
• Quantum K--theory of Grassmannians from a Yang-Baxter algebra
• Exotic Quantum Difference Equations and Integral Solutions