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Mathematics > Combinatorics

arXiv:1805.02287 (math)
[Submitted on 6 May 2018]

Title:Unique rectification in $d$-complete posets: towards the $K$-theory of Kac-Moody flag varieties

Authors:Rahul Ilango, Oliver Pechenik, Michael Zlatin
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Abstract: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.
Comments: 34 pages, 5 figures
Subjects: Combinatorics (math.CO); Algebraic Geometry (math.AG)
MSC classes: 05E15, 06A07, 14M15
Cite as: arXiv:1805.02287 [math.CO]
  (or arXiv:1805.02287v1 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1805.02287
Journal reference: Electronic Journal of Combinatorics 25(4), 2018, 1-35
Related DOI: https://doi.org/10.37236/7903

Submission history

From: Oliver Pechenik [view email]
[v1] Sun, 6 May 2018 22:36:13 UTC (35 KB)
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