Mathematische Zeitschrift

, Volume 266, Issue 2, pp 363–392

The shifted plactic monoid


DOI: 10.1007/s00209-009-0573-0

Cite this article as:
Serrano, L. Math. Z. (2010) 266: 363. doi:10.1007/s00209-009-0573-0


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.


Plactic monoid Shifted tableau Mixed insertion Schur P-function Shifted Littlewood–Richardson rule 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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