Crystals and trees: quasi-Kashiwara operators, monoids of binary trees, and Robinson--Schensted-type correspondences

@article{Cain2017CrystalsAT,
  title={Crystals and trees: quasi-Kashiwara operators, monoids of binary trees, and Robinson--Schensted-type correspondences},
  author={A. Cain and A. Malheiro},
  journal={arXiv: Combinatorics},
  year={2017}
}
  • A. Cain, A. Malheiro
  • Published 2017
  • Mathematics
  • arXiv: Combinatorics
  • Kashiwara's crystal graphs have a natural monoid structure that arises by identifying words labelling vertices that appear in the same position of isomorphic components. The celebrated plactic monoid (the monoid of Young tableaux), arises in this way from the crystal graph for the $q$-analogue of the general linear Lie algebra $\mathfrak{gl}_{n}$, and the so-called Kashiwara operators interact beautifully with the combinatorics of Young tableaux and with the Robinson--Schensted--Knuth… CONTINUE READING
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