Total positivity for cominuscule Grassmannians

Understand

In this paper we explore the combinatorics of the non-negative part (G/P)+ of a cominuscule Grassmannian.

• For each such Grassmannian we define Le-diagrams -- certain fillings of generalized Young diagrams which are in bijection with the cells of (G/P)+.
• In the classical cases, we describe Le-diagrams explicitly in terms of pattern avoidance.
• We also define a game on diagrams, by which one can reduce an arbitrary diagram to a Le-diagram.