Confluent KZ equations for sl_N with Poincare rank 2 at infinity

TL;DR

This paper develops confluent KZ equations with Poincare rank 2 at infinity for sl_N, providing integral solutions and connecting them to monodromy preserving deformation quantization.

Contribution

It introduces a new class of confluent KZ equations with Poincare rank 2 at infinity for sl_N, linking them to monodromy preserving deformation theory.

Findings

Constructed confluent KZ equations with Poincare rank 2 at infinity

Derived Hamiltonians from quantization of dlog tau

Provided integral representations for solutions

Abstract

We construct confluent KZ equations with Poincare rank 2 at infinity for the case of sl_N and the integral representation for the solutions. Hamiltonians of these confluent KZ equations are derived from suitable quantization of dlog tau constructed in the theory of monodromy preserving deformation by Jimbo, Miwa and Ueno. Our confluent KZ equations may be viewed as a quantization of monodromy preserving deformation with Poincare rank 2 at infinity.