Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Tuesday 5
Combinatorics
Christian Krattenthaler
› 10:00 - 10:30 (30min)
Affine type A geometric crystal structure on the Grassmannian
Gabriel Frieden  1  
1 : Department of Mathematics - University of Michigan
2074 East Hall, 530 Church Street, Ann Arbor, MI 48109-1043 -  États-Unis

We construct a type A(1) n−1 affine geometric crystal structure on the Grassmannian Gr(k, n). The tropicalization of this structure recovers the combinatorics of crystal operators on semistandard Young tableaux of rectangular shape (with n − k rows), including the affine crystal operator e 0. In particular, the promotion operation on these tableaux essentially corresponds to cyclically shifting the Plu ̈cker coordinates of the Grassmannian. 



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