Labelling Schubert intersections in the Grassmanian

Abstract

Points in the intersection of Schubert varieties are counted by various combinatorial objects, for example standard tableaux. This paper consider the problem of producing a natural labelling of intersection points by these combinatorial objects. When the Schubert varieties are being taken with respect to flags osculating at real points, several different methods have appeared implicitly in the literature (specifically in work of Mukhin-Tarasov-Varchenko, Speyer and Marcus). In this paper we show these various methods produce the same labelling and we describe it in an elementary way.