Geodesic
The intermediate orthogonal Lie algebra $\mathfrak b_{n-1/2}$ and its finite-dimensional representations
Izvestiya. Mathematics , Tome 62 (1998) no. 3, pp. 627-648.

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We suggest a method for separating multiple points of the spectrum in the reduction $B_n\downarrow B_{n-1}$ by introducing a non-semisimple intermediate subalgebra. We study the category of modules over this intermediate subalgebra that play the role of modules with highest weight. 
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V. V. Shtepin. The intermediate orthogonal Lie algebra $\mathfrak b_{n-1/2}$ and its finite-dimensional representations. Izvestiya. Mathematics , Tome 62 (1998) no. 3, pp. 627-648. http://geodesic.mathdoc.fr/item/IM2_1998_62_3_a7/

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