Symmetries of quantum Lax equations for the Painlev\'e equations

Understand

The Painlev\'e equations can be written as Hamiltonian systems with affine Weyl group symmetries.

• A canonical quantization of the Painlev\'e equations preserving the affine Weyl group symmetries has been studied.
• While, the Painlev\'e equations are isomonodromic equations for certain second-order linear differential equations.
• In this paper, we introduce a canonical quantization of Lax equations for the Painlev\'e equations and construct symmetries of the quantum Lax equations.