A weight basis for representations of even orthogonal Lie algebras (Q2741036)

The author constructs a basis for any finite dimensional representation of the Lie algebra \(\mathfrak o(2n)\). The basis differs from that of Gelfand and Tsetlin in the following ways: It is consistent with the chain of type D subalgebras \(\mathfrak o(2)\subset\mathfrak o(4)\subset\dots\subset\mathfrak o(2n-2) \subset\mathfrak o(2n)\) rather than with \(\mathfrak o(2)\subset\mathfrak o(3)\subset\dots \subset\mathfrak o(2n-1)\subset\mathfrak o(2n)\), so that the basis vectors can be chosen to be simultaneous weight vectors. However, the restriction from \(\mathfrak o(2n)\) to \(\mathfrak o(2n-2)\) is not multiplicity free. To separate the multiplicities, the author uses the irreducible action of the twisted Yangian \(Y^+(2)\) on the space \(V(\lambda)_{\mu}^+\) of highest weight vectors for \(\mathfrak o(2n-2)\) of weight \(\mu\) in the \(\mathfrak o(2n)\)-module \(V(\lambda)\) of highest weight \(\lambda\). In addition, he computes the action of a generating set of matrix elements on this basis, which is parametrized by Gelfand-Tsetlin patterns. NEWLINENEWLINENEWLINEThis paper follows a previous one [Commun. Math. Phys. 201, No. 3, 591-618 (1999; Zbl 0931.17005)], in which the author constructed a similar basis for the finite dimensional representations of the symplectic Lie algebras.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00024].