REU Project

Schubert calculus studies Schubert structure constants for the cohomology rings of a homogeneous space X. In many cases, combinatorial rules involving jeu de taquin on posets associated to these spaces have given positive formulas for these constants. Schutzenberger first proved such a rule for X a Grassmanian. Chaput and Perrin extended this to products of Λ-minuscule classes of spaces under a Kac-Moody group. This includes all Schubert classes for X a minuscule variety. Meanwhile, Buch, Samuel, Thomas, and Yong extended the jeu de taquin theory to the K-theory of all minuscule varieties. We begin to develop the analogous K-theoretic jeu de taquin theory for Proctor's d-complete posets, which are the associated posets for Λ-minuscule Schubert varieties.