Virtualization map for the Littelmann path model
arXiv:1509.08103 · doi:10.1007/s00031-017-9456-3
Abstract
We show the natural embedding of weight lattices from a diagram folding is a virtualization map for the Littelmann path model, which recovers a result of Kashiwara. As an application, we give a type independent proof that certain Kirillov--Reshetikhin crystals respect diagram foldings, which is a known result on a special case of a conjecture given by Okado, Schilling, and Shimozono.
14 pages, 1 figure; corrected statement of Theorem 4.2 in v3; minor corrections from referee report in v4