Plane partitions are a two-dimensional analogue of integer partitions introduced by MacMahon in the 1890s. Various generating functions for plane partitions admit beautiful product forms, displaying an unexpected connection to the representation theory of classical groups and Lie algebras. Cylindric partitions, defined by Gessel and Krattenthaler in the 1990s, are an affine analogue of plane partitions.

In this talk I will explain what cylindric partitions are, discuss their connection with the representation theory of infinite dimensional Lie algebras, and describe some recent results on Rogers--Ramanujan-type identities arising from the study of cylindric partitions. No knowledge of representation theory will be assumed in this talk.