Séminaire Lotharingien de Combinatoire, 82B.28 (2019), 12 pp.
Rahul Ilango, Oliver Pechenik, and Michael Zlatin
Unique rectification in d-complete posets
Abstract.
The jeu-de-taquin-based Littlewood-Richardson rule of Thomas-Yong (2009) for minuscule varieties has been extended in two orthogonal directions, either enriching the cohomology theory or else expanding the family of varieties considered. In one direction, Buch-Samuel (2016) developed a combinatorial theory of `unique rectification targets' in minuscule posets to extend the Thomas-Yong rule from ordinary cohomology to K-theory. Separately, Chaput-Perrin (2012) used the combinatorics of Proctor's `d-complete posets' to extend the Thomas-Yong rule from minuscule varieties to a broader class of Kac-Moody structure constants. We begin to address the unification of these theories. Our main result is the existence of unique rectification targets in a large class of d-complete posets. From this result, we obtain conjectural positive combinatorial formulas for certain K-theoretic Schubert structure constants in the Kac-Moody setting.
Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.
The following versions are available: