Geodesic
On the uniqueness of promotion operators on tensor products of type $A$ crystals
Journal of Algebraic Combinatorics, Tome 31 (2010) no. 2, pp. 217-251.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The affine Dynkin diagram of type $A _{ n } ^{(1)}$ has a cyclic symmetry. The analogue of this Dynkin diagram automorphism on the level of crystals is called a promotion operator. In this paper we show that the only irreducible type $A _{ n }$ crystals which admit a promotion operator are the highest weight crystals indexed by rectangles. In addition we prove that on the tensor product of two type $A _{ n }$ crystals labeled by rectangles, there is a single connected promotion operator. We conjecture this to be true for an arbitrary number of tensor factors. Our results are in agreement with Kashiwara's conjecture that all `good' affine crystals are tensor products of Kirillov-Reshetikhin crystals.
Keywords: keywords affine crystal bases, promotion operator, Schur polynomial factorization 
@article{JAC_2010__31_2_a3,
     author = {Bandlow, Jason and Schilling, Anne and Thi\'ery, Nicolas M.},
     title = {On the uniqueness of promotion operators on tensor products of type $A$ crystals},
     journal = {Journal of Algebraic Combinatorics},
     pages = {217--251},
     publisher = {mathdoc},
     volume = {31},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2010__31_2_a3/}
}
TY  - JOUR
AU  - Bandlow, Jason
AU  - Schilling, Anne
AU  - Thiéry, Nicolas M.
TI  - On the uniqueness of promotion operators on tensor products of type $A$ crystals
JO  - Journal of Algebraic Combinatorics
PY  - 2010
SP  - 217
EP  - 251
VL  - 31
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2010__31_2_a3/
LA  - en
ID  - JAC_2010__31_2_a3
ER  - 
%0 Journal Article
%A Bandlow, Jason
%A Schilling, Anne
%A Thiéry, Nicolas M.
%T On the uniqueness of promotion operators on tensor products of type $A$ crystals
%J Journal of Algebraic Combinatorics
%D 2010
%P 217-251
%V 31
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2010__31_2_a3/
%G en
%F JAC_2010__31_2_a3
Bandlow, Jason; Schilling, Anne; Thiéry, Nicolas M. On the uniqueness of promotion operators on tensor products of type $A$ crystals. Journal of Algebraic Combinatorics, Tome 31 (2010) no. 2, pp. 217-251. http://geodesic.mathdoc.fr/item/JAC_2010__31_2_a3/