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

D. V. Artamonov; V. A. Goloubeva

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arXiv · 1305.0987

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

D. V. Artamonov·V. A. Goloubeva

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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.

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BibTeX RIS

D. V. Artamonov, V. A. Goloubeva. 2013-05-05. Wigner coefficient for Lie algebras of series $B,C,D$ and a base of Gelfand-Tsetlin type. https://arxiv.org/abs/1305.0987

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