Symmetries of periodic and free boundary measures on partitions

There is a close connection between certain models of random integer partitions and random growth models in the KPZ universality class. I will give an introduction to these connections before discussing some new work establishing non-trivial symmetries of two particular models of random partitions. A special case was previously discovered by Imamura, Mucciconi, and Sasamoto, and was used to establish the Baik–Rains phase transition for an integrable polymer model in a half space. Our proof is new even in this special case.

This is based on joint work with Michael Wheeler.