Presentations of Principal Subspaces of Higher Level Standard A2(2)${A}_{2}^{(2)}$-Modules

Abstract

We study the principal subspaces of higher level standard ${A}_{2}^{(2)}$-modules, extending earlier work in the level one case, by Calinescu, Lepowsky and Milas. We prove natural presentations of principal subspaces and also of certain related spaces. By using these presentations we obtain exact sequences, which yield recursions satisfied by the characters of the principal subspaces and related spaces. We conjecture a formula for a specialized character of the principal subspace, given by the Nahm sum of the inverse of the tadpole Cartan matrix.