Quantum integrable systems and differential Galois theory

DOI10.1007/BF01234630zbMath0901.58021arXivalg-geom/9607012MaRDI QIDQ1383781

Dennis Gaitsgory, Pavel I. Etingof, Alexander Braverman

Publication date: 26 November 1998

Published in: Transformation Groups (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9607012

zbMATH Keywords

eigenvalue problemdifferential Galois group\(D\)-modulealgebraic integrabilityquantum completely integrable systems

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Applications of dynamical systems (37N99) Commutative rings of differential operators and their modules (13N10) Differential algebra (12H05) Curves in algebraic geometry (14H99)

Related Items (22)

Generalized Lennard-Jones potentials, SUSYQM and differential Galois theory ⋮ Differential Tannakian categories ⋮ Differential Galois theory and Darboux transformations for integrable systems ⋮ On rings of commuting partial differential operators ⋮ Parameterized Picard-Vessiot extensions and Atiyah extensions ⋮ Deformed Calogero-Moser operators and ideals of rational Cherednik algebras ⋮ The Schur-Sato theory for quasi-elliptic rings ⋮ On Algebraic Integrability of the Deformed Elliptic CalogeroMoser Problem ⋮ Commuting differential operators and higher-dimensional algebraic varieties ⋮ Difference Galois groups under specialization ⋮ Algebraic Geometric Properties of Spectral Surfaces of Quantum Integrable Systems and Their Isospectral Deformations ⋮ Factorization and resultants of partial differential operators ⋮ On elliptic Calogero-Moser systems for complex crystallographic reflection groups ⋮ Darboux transformations from the Appell-Lauricella operator ⋮ Commutative partial differential operators ⋮ The algebraic integrability of the quantum Toda lattice and the Radon transform ⋮ Tannakian categories, linear differential algebraic groups, and parametrized linear differential equations ⋮ Algebraic integrability of the two-body Ruijsenaars operator ⋮ Rational KdV potentials and differential Galois theory ⋮ Kernel inspired factorizations of partial differential operators ⋮ Algebraic Spectral Relations for Elliptic Quantum Calogero-Moser Problems ⋮ Spectral Picard-Vessiot fields for algebro-geometric Schrödinger operators

Cites Work

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• On the calculation of some differential Galois groups
• Integrability in the theory of Schrödinger operator and harmonic analysis
• Commutative rings of partial differential operators and Lie algebras
• Spherical functions on affine Lie groups
• Introduction to Grothendieck duality theory
• Commutative linear differential operators

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