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

TL;DR

This paper constructs Gelfand-Tsetlin type base vectors for the orthogonal Lie algebra ffff_{2n+1} using Z-invariants, revealing a relation between restriction problems in orthogonal and general linear algebras.

Contribution

It introduces a new method to construct base vectors for ffff_{2n+1} representations based on Z-invariants and restriction relations.

Findings

Constructed Gelfand-Tsetlin type base vectors for ffff_{2n+1}

Discovered relation between restriction problems in orthogonal and general linear algebras

Applied Z-invariants method to representation theory

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