Sylvain Carpentier

Publications

Difference Operators and Integrable Lattices

Construction and classification of integrable differential-difference equations through Lax operators, recursion operators, and Hamiltonian structures.

Arithmetic supports of Lax difference hierarchies
arXiv:2606.24273 (2026).
With A. Mikhailov and J.P. Wang,
PreHamiltonian and Hamiltonian operators for differential-difference equations
Nonlinearity 33 (2020).
With A. Mikhailov and J.P. Wang,
Rational recursion operators for integrable differential-difference equations
Communications in Mathematical Physics 370 (2019).

Algebraic Quantization of Integrable Lattices

Algebraic approaches to the quantization of discrete integrable systems, including the Volterra hierarchy and its noncommutative extensions.

With J.P. Wang and A.V. Mikhailov,
Integrable Volterra hierarchies over nonabelian algebras
arXiv:2607.17868 (2026).
With A. Mikhailov and J.P. Wang,
Algebraic quantization approach to integrable differential-difference equations
arXiv:2509.21775 (2025).
With A. Mikhailov and J.P. Wang,
Hamiltonians for the quantized Volterra hierarchy
Nonlinearity 37 (2024).
With A. Mikhailov and J.P. Wang,
Quantisations of the Volterra hierarchy
Letters in Mathematical Physics 112 (2022).

Classical Affine W-algebras

Realizations of classical W-algebras through reductions of integrable hierarchies and Adler-type operators.

With U. Suh,
Gelfand-Dickey realization of the supersymmetric W algebras for gl(n+1,n) and gl(n,n)
Nonlinearity 38 (2025).
With G. Lee and U. Suh,
Integrable systems on rectangular superalgebras via super Adler-type operators
Communications in Mathematical Physics 405 (2021).
With U. Suh,
Supersymmetric bi-Hamiltonian integrable systems
Communications in Mathematical Physics 382 (2021).
With A. De Sole, V. Kac, D. Valeri and J. van de Leur,
p-reduced multicomponent KP hierarchy and classical W-algebras
Communications in Mathematical Physics 380 (2020).

Differential Operators and Integrable PDEs

Rational differential operators, Hamiltonian structures, and Lax formulations for continuous integrable systems.

Lax-Sato formulation of the Novikov-Veselov hierarchy
Preprint (2020).
A sufficient condition for a rational differential operator to generate an integrable system
Japanese Journal of Mathematics 12 (2017).
Compatible Hamiltonian operators for the Krichever-Novikov equation
Comptes Rendus Mathématique 355 (2017).
With A. De Sole and V.G. Kac,
Singular degree of a rational matrix pseudodifferential operator
International Mathematics Research Notices (2015).
With A. De Sole and V.G. Kac,
Rational matrix pseudodifferential operators
Selecta Mathematica (2014).
With A. De Sole and V.G. Kac,
Some algebraic properties of differential operators
Journal of Mathematical Physics (2012).