Wigner coefficient for Lie algebras of series $B,C,D$ and a base of Gelfand-Tsetlin type

Abstract

For the Lie algebras $g_n={\mathfrak{o}}_{2n+1},{\mathfrak{sp}}_{2n},{\mathfrak{o}}_{2n}$ a simple construction of a base in an irreducible representation is given. The construction of this base uses the method of $Z$-invariants of Zhelobenko and the technique of Wigner coefficients, which was applied by Biedenharn and Baird to the construction of a Gelfand-Tsetlin base in the case ${\mathfrak{gl}}_n$. A relation between matrix elements and Wigner coefficients for $g_n$ and analogous objects for ${\mathfrak{gl}}_{n+1}$ is established.

arXiv comment54 pages