Solutions to Benoit and Saint-Aubin PDEs via hidden quantum group symmetry
Mon, Jan. 11th 2016, 11:00-12:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
I describe a systematic method for solving partial differential equations of Benoit \& Saint-Aubin type, 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, allowing 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 both CFT and SLEs. \\ \\ Joint work with Kalle Kytölä (Aalto University, Espoo) and Steven
Flores (University of Helsinki).