The Gelfand-Tsetlin-Zhelobenko base vectors for the series $B$

Abstract: In the paper using the method of $Z$-invariants of Zhelobenko we construct base vectors of Gelfand-Tsetlin type in a representation of $\mathfrak{o}{2n+1}$, based on restrictions $\mathfrak{o}{2n+1}\downarrow\mathfrak{o}{2n-1}$. The construction is based on a discovered relation between restriction problems $\mathfrak{o}{2n+1}\downarrow\mathfrak{o}{2n-1}$ and $\mathfrak{gl}{n+1}\downarrow\mathfrak{gl}_{n-1}$.