Capelli elements for the algebra \(\mathfrak g_{2}\)
The authors construct central elements (referred to as Capelli elements) in the universal enveloping algebra \(U({\mathfrak g}_2)\) of the simple Lie algebra \({\mathfrak g}_2\) in terms of sums of squares of Pfaffians of some matrices with entries belonging to \({\mathfrak g}_2\). A characterization of such elements in terms of vanishing properties is given and relations between them and higher Casimir elements are obtained.
scientific article; zbMATH DE number 6199368