Reverse Plane Partitions and Modules for the Preprojective Algebra

Anne Dranowski

Reverse plane partitions - or RPPs for short - are order reversing maps of minuscule posets in types ADE. We report on joint work in progress with Elek, Kamnitzer, Libman, and Morton-Ferguson in which we give a type independent proof that RPPs form a crystal. Moreover, we describe how the crystal structure on RPPs can be realized geometrically on Lusztig’s nilpotent variety L via a bijection between RPPs and "generic" modules for the preprojective algebra. Time permitting we explore the effects of toggling and RSK on irreducible components of L.

https://www.ias.edu/video/reverse-plane-partitions-and-modules-preprojective-algebra