Geodesic
Characters and dimensions of highest-weight representations of the intermediate Lie group $D_{n-1/2}$
Izvestiya. Mathematics , Tome 78 (2014) no. 3, pp. 621-639

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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.
Keywords: semiclassical intermediate Lie groups, finite-dimensional highest-weight representations, branching rules, weight basis, character and dimension of a representation of a Lie group. 
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     title = {Characters and dimensions of highest-weight representations of the intermediate {Lie} group $D_{n-1/2}$},
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V. V. Shtepin; D. L. Konashenkov. Characters and dimensions of highest-weight representations of the intermediate Lie group $D_{n-1/2}$. Izvestiya. Mathematics , Tome 78 (2014) no. 3, pp. 621-639. http://geodesic.mathdoc.fr/item/IM2_2014_78_3_a9/