Amitsur Symposium: Malka Schaps - "Symmetric Kashivara crystals of type A in low rank"

Tue, 26/06/201811:30-12:30
Manchester House, Lecture Hall 2
The basis of elements of the highest weight representations of affine Lie algebra of type A can be labeled in three different ways, my multipartitions, by piecewise linear paths in the weight space, and by canonical basis elements. The entire infinite basis is recursively generated from the highest weight vector of operators f_i from the Chevalley basis of the affine Lie algebra, and organized into a crystal called a Kashiwara crystal. We describe cases where one can move between the different labelings in a non-recursive fashion, particularly when the crystal has some symmetry. (Joint work with Ola Amara-Omari)