Symmetry for the spin highest weight module $V(\hat{I}{›}_n)$

Abstract

For an affine Lie algebra $\mathfrak{g}$ of type $A_{2n}^{(2)}$ we get a special set of partitions for the highest weight modules $V(\hat{I}›)$, where $\hat{I}›=\hat{I}{›}_n$, and we also get a some results for the canonical basis elements. We demonstrate a symmetry of weights with fixed $n$-content around the weights gotten from the empty partition by adding multiples of the null root. We also find the highest power of the quantum parameter $q$ in an important set of canonical basis elements.