Central elements in the universal enveloping algebra and function of matrix elements

Abstract

In the paper a construction of central elements in $U({\mathfrak{o}}_N)$ and $U({\mathfrak{g}}_2)$ based on invariant theory is given. New function of matrix elements that appear in description of the center of $U({\mathfrak{g}}_2)$ are defined.

17 pages, 9 figures