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

Abstract

Applying the quantum group method developed in [50], 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 [49, 55], 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.