Séminaire Lotharingien de Combinatoire, 80B.26 (2018), 12 pp.
Sami Assaf and Ezgi Kantarci Oğuz
Crystal Graphs for Shifted Tableaux
Abstract.
We define crystal operators on semistandard shifted tableaux, giving a
new proof that Schur P-functions are Schur positive. We define a
queer crystal operator to construct a connected queer crystal on
semistandard shifted tableaux of a given shape, providing a new proof
that products of Schur P-functions are Schur P-positive. We also
give a rectification map from shifted tableaux to Young tableaux that
commutes with the crystal operators and provides a dual algorithm to
shifted insertion.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
The following versions are available: