Kirillov--Reshetikhin modules associated to G_2

We define and study the Kirillov–Reshetikhin modules for algebras of type $G_2$. We compute the graded character of these modules and verify that they are in accordance with the conjectures in math.QA/981202 and math.QA/0102113. These results give the first complete description of families of Kirillov–Reshetikhin modules whose isotypical components have multiplicity bigger than one.