Intertwining operators for vertex representations of toroidal Lie algebras
A toroidal Lie algebra \(\tau_{[n]}\) is the universal central extension of the Lie algebra \({\mathbf g} \otimes {\mathbb C} [ t_1 ^{\pm}, \cdots, t_n ^{\pm}]\), where \(\mathbf g\) is the finite dimensional simple Lie algebra over \({\mathbb C}\). When \(n=1\), \(\tau_{[1]}\) is an affine Lie algebra. In [\textit{S. Eswara Rao} and \textit{R. V. Moody}, Commun. Math. Phys. 159, 239-264 (1994; Zbl 0808.17018)] a vertex operator representation of \(\tau_{[n]}\) was constructed. In the paper under review the authors construct intertwining operators for the vertex representations of \(\tau_{[n]}\) and investigate how the intertwining operators depend on the way of labelling the points in the dual \({\mathbb Z} ^{n}\) of the torus \(T^{n}\).
scientific article; zbMATH DE number 1202533