A weight basis for representations of even orthogonal Lie algebras

A weight basis for each finite-dimensional irreducible representation of the orthogonal Lie algebra o(2n) is constructed. The basis vectors are parametrized by the D-type Gelfand–Tsetlin patterns. Explicit formulas for the matrix elements of generators of o(2n) in this basis are given. The construction is based on the representation theory of the Yangians and extends our previous results for the symplectic Lie algebras.