Mathematische Zeitschrift

, Volume 266, Issue 2, pp 363–392

The shifted plactic monoid

Article

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.

Keywords

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

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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