Mathematische Zeitschrift

, Volume 266, Issue 2, pp 363–392

The shifted plactic monoid

Authors

    • Department of MathematicsUniversity of Michigan
Article

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

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 monoidShifted tableauMixed insertionSchur P-functionShifted Littlewood–Richardson rule

Copyright information

© Springer-Verlag 2009