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

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.

46 pages, 17 figures. v4(final, published)

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• Conformal Random Geometry
• Critical percolation in the plane
• Smirnov's observable for free boundary conditions, interfaces and crossing probabilities
• The scaling limit of two cluster boundaries in critical lattice models
• Conformal blocks, $q$-combinatorics, and quantum group symmetry
• SLE, CFT and zig-zag probabilities
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Cited by in corpus (5)

• Multiple SLE type scaling limits: from local to global
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• Standard modules, radicals, and the valenced Temperley-Lieb algebra
• Scaling Limits of Crossing Probabilities in Metric Graph GFF
• Planar UST Branches and $c=-2$ Degenerate Boundary Correlations