Quantum K-theory of Quiver Varieties and Many-Body Systems

Abstract

We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit which produces a K-theoretic version of results of Givental and Kim, connecting quantum geometry of flag varieties and Toda lattice.

v5: 34 pages, published version

References in corpus (4)

• Defects and Quantum Seiberg-Witten Geometry
• Baxter Q-operator from quantum K-theory
• $(SL(N),q)$-opers, the $q$-Langlands correspondence, and quantum/classical duality
• Toroidal q-Opers

Cited by in corpus (13)

• BPS Indices, Modularity and Perturbations in Quantum K-theory
• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• 3d Mirror Symmetry for Instanton Moduli Spaces
• Toroidal q-Opers
• Quantum K theory rings of partial flag manifolds
• Quantum K theory of Grassmannians, Wilson line operators, and Schur bundles
• Decomposition squared
• ${\text{AdS}}_4$ Holography and the Hilbert Scheme
• q-Opers, QQ-systems, and Bethe Ansatz II: Generalized Minors
• Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials
• Opers on the projective line, Wronskian relations, and the Bethe Ansatz
• Quantum K-theory and Integrability
• Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials