arXiv subjects

V. A. Goloubeva

Publications and source records attributed to V. A. Goloubeva.

3 recordsLinked to original sources

arXiv2013

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

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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arXiv2012

Knizhnik-Zamolodchikov type equations for the root system $B$ and Capelli central elements

The construction of the well-known Knizhnik-Zamolodchikov equations uses the central element of the second order in the universal enveloping algebra for some Lie algebra. But in the universal enveloping algebra there are central elements of higher orders. It seems desirable to use these elements for the construction of Knizhnik-Zamolodchikov type equations. In the present paper we give a construction of such Knizhnik-Zamolodchikov type equations for the root system $B$ associated with Capelli central elements in the universal enveloping algebra for the orthogonal algebra.

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arXiv2012

Noncommutative pfaffians and representations

Noncommutative pfaffians associated with an orthogonal algebra are some special elements of the universal enveloping algebra. In the paper it is suggested to use some pfaffians as raising operators. The images of these pfaffians in the Mickelson-Zhelobenko algebra are calculated. It allows to find a place of pfaffians among other raising operators. As a byproduct the action of the pfaffians on the Gelfand-Tsetlin-Molev bases is found. The action of pfaffians in the tensor realization of representation is considered in the appendix.

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