%0 Journal Article %T Vertex-algebraic structure of principal subspaces of standard A_2^{(2)}-modules, I %A Corina Calinescu %A James Lepowsky %A Antun Milas %J Mathematics %D 2014 %I arXiv %X Extending earlier work of the authors, this is the first in a series of papers devoted to the vertex-algebraic structure of principal subspaces of standard modules for twisted affine Kac-Moody algebras. In this part, we develop the necessary theory of principal subspaces for the affine Lie algebra A_2^{(2)}, which we expect can be extended to higher rank algebras. As a "test case," we consider the principal subspace of the basic A_2^{(2)}-module and explore its structure in depth. %U http://arxiv.org/abs/1402.3026v2