Eveliina Peltola: Solutions to Benoit and Saint-Aubin PDEs via hidden quantum group symmetry

I describe a method for solving Benoit and Saint-Aubin partial differential equations, PDEs which arise in conformal field theory (CFT) and in the theory of Schramm-Loewner evolutions (SLE). An important feature of our method is the systematic construction of solutions with boundary conditions given by specified asymptotic behavior. This allows one to explicitly find particular solutions, such as conformal blocks, multiple SLE pure partition functions, and chordal SLE boundary visit (zig-zag) probability amplitudes. Our method is a correspondence associating vectors in a tensor product representation of a quantum group to Coulomb gas type integral functions, in which properties of the functions are encoded in natural, representation theoretical properties of the vectors. I discuss the core idea of the method and applications to SLE and CFT.

Joint work with Kalle Kytölä (Aalto University, Espoo) and Steven Flores (University of Helsinki).