Geodesic
Crystal Graphs for Shifted Tableaux
Séminaire lotharingien de combinatoire, 80B (2018)
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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. 

@article{SLC_2018_80B_a25,
     author = {Sami Assaf and Ezgi Kantarci O\u{g}uz},
     title = {Crystal {Graphs} for {Shifted} {Tableaux}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2018},
     volume = {80B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a25/}
}
TY  - JOUR
AU  - Sami Assaf
AU  - Ezgi Kantarci Oğuz
TI  - Crystal Graphs for Shifted Tableaux
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a25/
ID  - SLC_2018_80B_a25
ER  - 
%0 Journal Article
%A Sami Assaf
%A Ezgi Kantarci Oğuz
%T Crystal Graphs for Shifted Tableaux
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a25/
%F SLC_2018_80B_a25
Sami Assaf; Ezgi Kantarci Oğuz. Crystal Graphs for Shifted Tableaux. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a25/