Kirillov--Reshetikhin crystals for nonexceptional types

Abstract

We provide combinatorial models for all Kirillov--Reshetikhin crystals of nonexceptional type, which were recently shown to exist. For types D_n^(1), B_n^(1), A_{2n-1}^(2) we rely on a previous construction using the Dynkin diagram automorphism which interchanges nodes 0 and 1. For type C_n^(1) we use a Dynkin diagram folding and for types A_{2n}^(2), D_{n+1}^(2) a similarity construction. We also show that for types C_n^(1) and D_{n+1}^(2) the analog of the Dynkin diagram automorphism exists on the level of crystals.