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 ${\mathfrak{gl}}_{n+1}\downarrow {\mathfrak{gl}}_{n-1}$.

21 pages. arXiv admin note: text overlap with arXiv:1607.08704; in the second version a comparision with Molev's approach is removed

References in corpus (1)

• The comparison Gelfand-Tsetlin-Molev and Gelfand-Tsetlin-Zhelobenko bases for ${\mathfrak{sp}}_{2n}$