Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson–Schensted–Knuth-type correspondence for quasi-ribbon tableaux

@article{Cain2016CrystallizingTH,
  title={Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson–Schensted–Knuth-type correspondence for quasi-ribbon tableaux},
  author={A. Cain and A. Malheiro},
  journal={Journal of Algebraic Combinatorics},
  year={2016},
  volume={45},
  pages={475-524}
}
  • A. Cain, A. Malheiro
  • Published 2016
  • Mathematics
  • Journal of Algebraic Combinatorics
  • Crystal graphs, in the sense of Kashiwara, carry a natural monoid structure given by identifying words labelling vertices that appear in the same position of isomorphic components of the crystal. In the particular case of the crystal graph for the q-analogue of the special linear Lie algebra $$\mathfrak {sl}_{n}$$sln, this monoid is the celebrated plactic monoid, whose elements can be identified with Young tableaux. The crystal graph and the so-called Kashiwara operators interact beautifully… CONTINUE READING
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    References

    SHOWING 1-10 OF 51 REFERENCES
    The Lexicographic Cross-Section of the Plactic Monoid Is Regular
    • 6
    • PDF
    Group Characters and Algebra
    • 304
    • PDF
    On the hypoplactic monoid
    • J. Novelli
    • Mathematics, Computer Science
    • Discret. Math.
    • 2000
    • 38
    Noncommutative symmetric functions
    • 425
    • PDF
    Crystals For Dummies
    • 12
    • PDF