Coulomb Gas and Spin Chain: Quantum Group Applications

This lecture discusses the interplay between Coulomb gas models and spin chains within the framework of quantum groups. The instructor begins by recapping the general picture of spin chains as tensor product modules of quantum groups, specifically focusing on Uq(51(2,C)). The discussion includes the mathematical formulation of Coulomb gas charges and their relation to quantum group modules. The instructor emphasizes the importance of contour choices in defining meaningful objects in random geometry, particularly in the context of crossing probabilities in SLE (Stochastic Loewner Evolution) models. The lecture also highlights the algebraic structure underlying these choices, linking them to differential equations and the properties of highest weight vectors. The instructor presents various properties and theorems related to the BPC (Burgers-Poisson-Cauchy) equations, emphasizing their relevance in solving problems related to SLE. The lecture concludes with a discussion on the implications of these findings for understanding multiple interfaces in critical models, particularly in the context of the easing model and its scaling limits.