Kirillov--Reshetikhin crystals for nonexceptional types

TL;DR

This paper constructs combinatorial models for all Kirillov--Reshetikhin crystals of nonexceptional types, expanding understanding of their structure and symmetries using various algebraic techniques.

Contribution

It provides explicit combinatorial models for nonexceptional Kirillov--Reshetikhin crystals, including new symmetry results for certain types.

Findings

Models for all nonexceptional Kirillov--Reshetikhin crystals are constructed.

Dynkin diagram automorphisms are shown to exist at the crystal level for specific types.

New folding and similarity constructions are introduced for certain 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.