Geodesic
Promotion, Evacuation and Cactus Groups
Séminaire lotharingien de combinatoire, 78B (2017)

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The promotion operator on rectangular standard tableaux can be generalised to an operator acting on the invariant highest weight words in the tensor power of a crystal. For the vector representation of a symplectic group the Sundaram correspondence is an injective map to perfect matchings. We show that this map intertwines promotion and rotation. For the adjoint representation of a general linear group we construct a similar map to permutations. We show that this map also intertwines promotion and rotation. These results are proved using an approach to the action of the cactus group using a generalisation of local rules and growth diagrams. 

@article{SLC_2017_78B_a70,
     author = {Stephan Pfannerer and Martin Rubey and Bruce W. Westbury},
     title = {Promotion, {Evacuation} and {Cactus} {Groups}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a70/}
}
TY  - JOUR
AU  - Stephan Pfannerer
AU  - Martin Rubey
AU  - Bruce W. Westbury
TI  - Promotion, Evacuation and Cactus Groups
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a70/
ID  - SLC_2017_78B_a70
ER  - 
%0 Journal Article
%A Stephan Pfannerer
%A Martin Rubey
%A Bruce W. Westbury
%T Promotion, Evacuation and Cactus Groups
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a70/
%F SLC_2017_78B_a70
Stephan Pfannerer; Martin Rubey; Bruce W. Westbury. Promotion, Evacuation and Cactus Groups. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a70/