Invariant differential operators for noncompact Lie groups: The Sp(n,1) case

Abstract

In this paper, we continue the project of systematic construction of invariant differential operators (IDOs) on the example of the noncompact algebras $sp(n,1)$. Our choice of these algebras is motivated by the fact that they belong to a narrow class of algebras, which are of split rank one, of which class the other cases were studied, some long time ago. We concentrate on the case $n=2$. We give the main multiplets and the main reduced multiplets of indecomposable elementary representations (ER) for, including the necessary data for all relevant invariant differential operators. We also present explicit expressions for the singular vectors and the intertwining differential operators.