Reading’s shard intersection order is a lattice structure on a finite Coxeter group which is weaker than the weak order. This structure also appears in the representation theory of finite-dimensional algebras as the inclusion order on certain subcategories of modules. Algebraically, the cover relations of this lattice are traversed by applying a “reduction operation” associated to a chosen module. In this talk, we explain the combinatorial analog of this reduction operation in type A. No prior knowledge of finite-dimensional algebras or the shard intersection order will be assumed.

Speaker’s webpage: https://sites.google.com/view/erichanson/