Tensor Products of a Finite-Dimensional Representation and an Infinite-Dimensional Representation
Abstract
In this project, we explicitly find the decomposition of the tensor product of a Verma module $Z(\lambda)$ and the standard module ${\mathbb C}^n$ of the Lie algebras $\mathfrak{sl}(n)$, $n=2,3$. The result provides an explicit description of the translation functor introduced by Bernstein and Gelfand.