Symmetries of Periodic and Free Boundary Measures on Partitions

This lecture from the Harvard CMSA program on "Classical, quantum, and probabilistic integrable systems – novel interactions and applications" features speaker Jimmy He from Ohio State University discussing symmetries in probability measures on partitions. Explore the mathematical foundations of periodic and free boundary q-Whittaker measures, which are defined using q-Whittaker functions and a parameter u that controls boundary behavior. Learn about a hidden distributional symmetry that exchanges the u and q parameters, along with related results on Hall-Littlewood measures. The talk also covers identities previously established by Imamura–Mucciconi–Sasamoto, presenting work conducted jointly with Michael Wheeler.