Schur’s $Q$-functions and Twisted Affine Lie Algebras

Abstract

Weight vectors of the basic representations of $A^{(2)}_{2\ell}$ and $D^{(2)}_{\ell+1}$ are studied. They are expressed in terms of Schur’s $Q$-functions. The up and down motion along the string of the fundamental imaginary root is described as a combinatorial game.