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Title: Unique Rectification in $d$-Complete Posets: Towards the $K$-Theory of Kac-Moody Flag Varieties
The jeu-de-taquin-based Littlewood-Richardson rule of H. Thomas and A. 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, A. Buch and M. 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, P.-E. Chaput and N. Perrin (2012) used the combinatorics of R. 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.  more » « less
Award ID(s):
1703696
NSF-PAR ID:
10216215
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
The Electronic Journal of Combinatorics
Volume:
25
Issue:
4
ISSN:
1077-8926
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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