Center of Kostant algebra

In this note, following Muić-Savin, we compute the center of Kostant algebra, introduced by Kostant in 1975 as strongly commuting algebra.

We explain how it encodes information on tensor products between a finite-dimensional and a Verma module, and about the structure of principal series representations via the work of Bernstein-Gelfand.

We also discuss conjectured relationships to Langlands duality.