Characters and dimensions of highest-weight representations of the intermediate Lie group $D_{n-1/2}$

We study highest-weight representations of the non-semisimple complex Lie group $D_{n-1/2}$ used for separating multiple points of the spectrum in the reduction $D_n\downarrow D_{n-1}$. In particular, we find formulae for the characters and dimensions of these representations, which turn out to be similar to the well-known Weyl formulae for classical Lie groups.