Abstract
We introduce a shifted analog of the plactic monoid of Lascoux and Schützenberger, the shifted plactic monoid. It can be defined in two different ways: via the shifted Knuth relations, or using Haiman’s mixed insertion. Applications include: a new combinatorial derivation (and a new version of) the shifted Littlewood–Richardson Rule; similar results for the coefficients in the Schur expansion of a Schur P-function; a shifted counterpart of the Lascoux–Schützenberger theory of noncommutative Schur functions in plactic variables; a characterization of shifted tableau words; and more.
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This work was partially supported by NSF grant DMS-0555880 and by an NSERC Postgraduate Scholarship.
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Serrano, L. The shifted plactic monoid. Math. Z. 266, 363–392 (2010). https://doi.org/10.1007/s00209-009-0573-0
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DOI: https://doi.org/10.1007/s00209-009-0573-0