  We prove a conjecture in \cite{L} stating that certain polynomials
$P^{\sigma}_{y,w}(q)$ introduced in \cite{LV1} for twisted involutions in an
affine Weyl group give $(-q)$-analogues of weight multiplicities of the
Langlands dual group $\check{G}$. We also prove that the signature of a
naturally defined hermitian form on each irreducible representation of
$\check{G}$ can be expressed in terms of these polynomials
$P^{\sigma}_{y,w}(q)$.
