Tutte seminar - Kevin Purbhoo

Promotion for Staircase Tableaux

Abstract:

Promotion is one of the fundamental operations on standard young tableaux. It has received a fair bit of attention recently because of its relevance in representation theory, and its intriguing combinatorial structure. In 2010, Rhoades proved a theorem that the describes the orbit structure of promotion on tableaux of rectangular shape, and since then there have been several other proofs of this result. In this talk, I will discuss some new results about promotion on staircase shapes. These are proved using geometric ideas, and are essentially attributable to the existence of some very special subvarieties of a Grassmannian.