Classification of irreducible non-dense modules for \(A_{2}^{\left(2\right)}\)

Abstract

We obtain a classification of the supports of irreducible \(A_{2}^{\left(2\right)}\)-modules. In particular, we get a classification of all non-dense irreducible \(A_{2}^{\left(2\right)}\)-modules with at least one finite-dimensional weight subspace.