Combinatorial bases of standard modules of twisted affine Lie algebras in types $A_{2l-1}^{(2)}$ and $D_{l+1}^{(2)}$: rectangular highest weights

Abstract: We consider the standard modules of rectangular highest weights of affine Lie algebras in types $A_{2l-1}^{(2)}$ and $D_{l+1}^{(2)}$. By using vertex algebraic techniques we construct the combinatorial bases for standard modules and their principal subspaces and parafermionic spaces. Finally, we compute the corresponding character formulae and, as an application, we obtain two new families of combinatorial identities.