The Schur-Sato theory for quasi-elliptic rings

DOI10.1134/s0081543823010078zbMath1527.13031arXiv2205.06790OpenAlexW4379511864MaRDI QIDQ6156019

Alexander Zheglov

Publication date: 9 June 2023

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.06790

zbMATH Keywords

algebraic surfacesalgebraic curvesquantum integrable systemsBirkhoff decompositionpseudo-differential operatorsnoncommutative ringsKdV equationsSchur operatorsSchur pairsKrichever correspondencerings of operatorsspectral moduleAbhyankar's inversion formulaprojective spectral dataquasi-elliptic ringsSato operatorsslice decomposition

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Linear ordinary differential equations and systems (34A30) Relationships between algebraic curves and integrable systems (14H70) Surfaces and higher-dimensional varieties (14J99) Commutative rings of differential operators and their modules (13N10) Rings of differential operators (associative algebraic aspects) (16S32)

Cites Work

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• Commuting differential operators and higher-dimensional algebraic varieties
• Loop groups and equations of KdV type
• Solvability of the super KP equation and generalized of the Birkhoff decomposition
• Algebraic aspects of nonlinear differential equations
• The spectrum of difference operators and algebraic curves
• Commutative subrings of certain noncommutative rings
• Algebraic integrability for the Schrödinger equation and finite reflection groups
• Quantum integrable systems and differential Galois theory
• Cherednik algebras and differential operators on quasi-invariants.
• Commutative rings of partial differential operators and Lie algebras
• Discretization of commuting ordinary differential operators of rank 2 in the case of elliptic spectral curves
• Difference Krichever-Novikov operators of rank 2
• Endomorphisms of Weyl algebra and \(p\)-curvatures.
• On some questions related to the Krichever correspondence
• INTEGRABLE SYSTEMS AND LOCAL FIELDS
• On rings of commuting partial differential operators
• CATEGORY OF VECTOR BUNDLES ON ALGEBRAIC CURVES AND INFINITE DIMENSIONAL GRASSMANNIANS
• The Jacobian conjecture: Reduction of degree and formal expansion of the inverse
• Geometric properties of commutative subalgebras of partial differential operators
• FORMAL GROUPS ARISING FROM FORMAL PUNCTURED RIBBONS
• Formal punctured ribbons and two-dimensional local fields
• METHODS OF ALGEBRAIC GEOMETRY IN THE THEORY OF NON-LINEAR EQUATIONS
• Lagrange inversion in higher dimensions and umbral operators
• Commutative rings of ordinary linear differential operators
• New integrable generalizations of Calogero–Moser quantum problem
• On a relative version of the Krichever correspondence
• Commutative ordinary differential operators. II.—The identity P ⁿ = Q ^m
• Surprising examples of nonrational smooth spectral surfaces
• On divisors of small canonical degree on Godeaux surfaces
• Krichever correspondence for algebraic varieties
• Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles
• Fourier–Mukai transform on Weierstrass cubics and commuting differential operators
• Cohen–Macaulay modules over the algebra of planar quasi–invariants and Calogero–Moser systems
• Algebraic Geometric Properties of Spectral Surfaces of Quantum Integrable Systems and Their Isospectral Deformations
• Algebro-geometric Schrödinger operators in many dimensions
• Commutative partial differential operators
• The Krichever correspondence for algebraic surfaces