Quantum \(K\)-theory of quiver varieties and many-body systems

DOI10.1007/s00029-021-00698-3zbMath1478.19005arXiv1705.10419OpenAlexW3196612940MaRDI QIDQ821039

Petr P. Pushkar, Andrey V. Smirnov, Anton M. Zeitlin, Peter Koroteev

Publication date: 20 September 2021

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.10419

zbMATH Keywords

asymptotic of vertex functionsquantum \(K\)-theory of quiver varietiesquantum tautological classesspectrum of the quantum multiplication

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Supersymmetric field theories in quantum mechanics (81T60) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Exactly solvable models; Bethe ansatz (82B23) Representations of quivers and partially ordered sets (16G20) Classical groups (algebro-geometric aspects) (14L35) Equivariant (K)-theory (19L47)

Related Items (24)

TOROIDAL q-OPERS ⋮ Capped vertex with descendants for zero dimensional \(A_\infty\) quiver varieties ⋮ Quantum \(K\) theory of symplectic Grassmannians ⋮ Pursuing quantum difference equations. I: Stable envelopes of subvarieties ⋮ 3D mirror symmetry for instanton moduli spaces ⋮ Mirror symmetry and line operators ⋮ Quantum Lax pairs via Dunkl and Cherednik operators ⋮ \(q\)-opers, \(QQ\)-systems, and Bethe ansatz II: generalized minors ⋮ Calogero-Moser eigenfunctions modulo \(p^s\) ⋮ Grothendieck lines in 3d \(\mathcal{N} = 2\) SQCD and the quantum K-theory of the Grassmannian ⋮ Quantum K theory rings of partial flag manifolds ⋮ Virtual Coulomb branch and vertex functions ⋮ Quantum difference equation for Nakajima varieties ⋮ BPS/CFT correspondence. IV: Sigma models and defects in gauge theory ⋮ The quantum DELL system ⋮ Quantum K-theory of Grassmannians and non-abelian localization ⋮ A conjectural Peterson isomorphism in \(K\)-theory ⋮ Elliptic stable envelope for Hilbert scheme of points in the plane ⋮ Quantum K-theory of Calabi-Yau manifolds ⋮ Three-dimensional mirror self-symmetry of the cotangent bundle of the full flag variety ⋮ 3d mirror symmetry and quantum \(K\)-theory of hypertoric varieties ⋮ Twisted indices of 3d \( \mathcal{N}=4 \) gauge theories and enumerative geometry of quasi-maps ⋮ BPS indices, modularity and perturbations in quantum K-theory ⋮ Dualities in quantum integrable many-body systems and integrable probabilities. I.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Trigonometric version of quantum-classical duality in integrable systems
• On three dimensional quiver gauge theories and integrability
• KZ characteristic variety as the zero set of classical Calogero-Moser Hamiltonians
• Stable quasimaps to GIT quotients
• Quantum integrability and generalised quantum Schubert calculus
• Quantum cohomology of the Springer resolution
• On \(q\)-deformed \(\mathfrak{gl}_{\ell+1}\)-Whittaker function. III
• Quantum toroidal and shuffle algebras
• Baxter's relations and spectra of quantum integrable models
• Virtual fundamental classes via dg-manifolds
• A new class of integrable systems and its relation to solitons
• Action-angle maps and scattering theory for some finite-dimensional integrable systems. I: The pure soliton case
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• Quantum affine algebras and holonomic difference equations
• The intrinsic normal cone
• Quantum \(K\)-theory on flag manifolds, finite-difference Toda lattices and quantum groups
• Quantum \(K\)-theory. I: Foundations
• Kirwan surjectivity for quiver varieties
• Quantum cohomology of flag manifolds and Toda lattices
• \((\text{SL}(N), q)\)-opers, the \(q\)-Langlands correspondence, and quantum/classical duality
• Baxter \(Q\)-operator from quantum \(K\)-theory
• Trigonometric weight functions as \(K\)-theoretic stable envelope maps for the cotangent bundle of a flag variety
• Quantum geometry and quiver gauge theories
• Defects and quantum Seiberg-Witten geometry
• On the perturbation theory of closed linear operators
• Semi-infinite Schubert varieties and quantum 𝐾-theory of flag manifolds
• Quantum Integrability and Supersymmetric Vacua
• Quiver varieties and finite dimensional representations of quantum affine algebras
• Lectures on K-theoretic computations in enumerative geometry
• Quantum $q$-Langlands Correspondence
• Lectures on the integrability of the 6-vertex model
• Lectures on Nakajima's Quiver Varieties
• Quantum groups and quantum cohomology
• Quasimap counts and Bethe eigenfunctions

This page was built for publication: Quantum \(K\)-theory of quiver varieties and many-body systems