Department of Mathematics Calendar
Travis Scrimshaw, University of Queensland, Towards a uniform model for higher level Kirillov-Reshetikhin crystals
Kirillov-Reshetikhin (KR) modules are a special class of finite-dimensional modules for affine Lie algebras that have deep connections with mathematical physics. One important aspect is that they are conjectured to have crystal bases, which is known except for affine type E and F (and its dual). One of the open problems in KR crystals is to determine a combinatorial model for all KR crystals uniformly for all levels. There is a uniform construction for all level 1 KR crystals due to Kashiwara using extremal level-zero crystals, and this construction has been given explicitly for a few combinatorial models for crystals, such as with LS paths. In joint work with Cristian Lenart, we make some progress on this open problem by using Demazure crystals of affine Lie algebras and taking a tensor product of level 1 KR crystals.