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 2 n − 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 2 n ( 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.