Geodesic
Unique rectification in \(d\)-complete posets: towards the \(K\)-theory of Kac-Moody flag varieties
Rahul Ilango1 ; Oliver Pechenik2 ; Michael Zlatin1
1Rutgers University
2University of Michigan
The electronic journal of combinatorics, Tome 25 (2018) no. 4
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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.
DOI : 10.37236/7903
Classification : 06A07, 14M15
Mots-clés : unique rectification target, jeu de taquin, \(d\)-complete poset, Schubert calculus, Kac-Moody group

Rahul Ilango  1   ; Oliver Pechenik  2   ; Michael Zlatin  1

1 Rutgers University
2 University of Michigan 
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Rahul Ilango; Oliver Pechenik; Michael Zlatin. Unique rectification in \(d\)-complete posets: towards the \(K\)-theory of Kac-Moody flag varieties. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/7903

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