We give local axioms that uniquely characterize the crystal-like structure on shifted tableaux developed by the authors and Purbhoo. These axioms closely resemble those developed by Stembridge for type A tableau crystals. This axiomatic characterization gives rise to a new method for proving and understanding Schur $Q$-positive expansions in symmetric function theory, just as the Stembridge axiomatic structure provides for ordinary Schur positivity.
@article{10_37236_8033,
author = {Maria Gillespie and Jake Levinson},
title = {Axioms for shifted tableau crystals},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {2},
doi = {10.37236/8033},
zbl = {1414.05296},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8033/}
}
TY - JOUR
AU - Maria Gillespie
AU - Jake Levinson
TI - Axioms for shifted tableau crystals
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/8033/
DO - 10.37236/8033
ID - 10_37236_8033
ER -
%0 Journal Article
%A Maria Gillespie
%A Jake Levinson
%T Axioms for shifted tableau crystals
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/8033/
%R 10.37236/8033
%F 10_37236_8033
Maria Gillespie; Jake Levinson. Axioms for shifted tableau crystals. The electronic journal of combinatorics, Tome 26 (2019) no. 2. doi: 10.37236/8033
