Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4655400 | Journal of Combinatorial Theory, Series A | 2013 | 25 Pages |
Abstract
On the polytope defined by Feigin, Fourier and Littelmann, associated to any highest weight corresponding to a rectangular partition, we define a crystal structure of type AnAn. We show that this crystal is isomorphic to the one obtained from Kashiwaraʼs crystal bases theory. Further we define on this polytope a bijective map and show that this map satisfies the properties of a weak promotion operator. This implies in particular that we provide an explicit realization of Kirillov–Reshetikhin crystals for the affine type An(1) via polytopes.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Deniz Kus,