Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga