Basis for solutions of the Benoit & Saint-Aubin PDEs with particular asymptotic properties

TL;DR

This paper constructs solutions to Benoit & Saint-Aubin PDEs with specific asymptotic boundary conditions using quantum group methods, generalizing previous pure partition function solutions related to multiple SLEs.

Contribution

It introduces a quantum group approach to solve Benoit & Saint-Aubin PDEs with recursive asymptotics, extending prior solutions to more complex systems of random curves.

Findings

Solutions generalize pure partition functions of multiple SLEs

Method employs quantum group techniques and fusion concepts

Results enable modeling of multiple curves emerging from the same point

Abstract

Applying the quantum group method developed in [KP20], we construct solutions to the Benoit & Saint-Aubin partial differential equations with boundary conditions given by specific recursive asymptotics properties. Our results generalize solutions constructed in [KP16, PW19], known as the pure partition functions of multiple Schramm-Loewner evolutions. The generalization is reminiscent of fusion in conformal field theory, and our solutions can be thought of as partition functions of systems of random curves, where many curves may emerge from the same point.