Geodesic
An action of the cactus group on shifted tableau crystals
Inês Rodrigues1
1CEAFEL, Faculty of Sciences, University of Lisbon
The electronic journal of combinatorics, Tome 30 (2023) no. 4
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

Recently, Gillespie, Levinson and Purbhoo introduced a crystal-like structure for shifted tableaux, called the shifted tableau crystal. We introduce, on this structure, a shifted version of the crystal reflection operators, which coincide with the restrictions of the shifted Schützenberger involution to any primed interval of two adjacent letters. Unlike type $A$ Young tableau crystals, these operators do not realize an action of the symmetric group on the shifted tableau crystal since the braid relations do not need to hold. Following a similar approach as Halacheva, we exhibit a natural internal action of the cactus group on this crystal, realized by the restrictions of the shifted Schützenberger involution to all primed intervals of the underlying crystal alphabet, containing, in particular, the aforesaid action of the shifted crystal reflection operator analogues.
DOI : 10.37236/9720
Classification : 05E18, 05E10, 05E05, 14M15, 14N15
Mots-clés : cactus group, shifted tableau, crystals

Inês Rodrigues  1

1 CEAFEL, Faculty of Sciences, University of Lisbon 
@article{10_37236_9720,
     author = {In\^es Rodrigues},
     title = {An action of the cactus group on shifted tableau crystals},
     journal = {The electronic journal of combinatorics},
     year = {2023},
     volume = {30},
     number = {4},
     doi = {10.37236/9720},
     zbl = {1535.05269},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9720/}
}
TY  - JOUR
AU  - Inês Rodrigues
TI  - An action of the cactus group on shifted tableau crystals
JO  - The electronic journal of combinatorics
PY  - 2023
VL  - 30
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.37236/9720/
DO  - 10.37236/9720
ID  - 10_37236_9720
ER  - 
%0 Journal Article
%A Inês Rodrigues
%T An action of the cactus group on shifted tableau crystals
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/9720/
%R 10.37236/9720
%F 10_37236_9720
Inês Rodrigues. An action of the cactus group on shifted tableau crystals. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/9720

Cité par Sources :