Intertwining differential operators for $\textrm {Mp}(n, \textbf {R})$ and $\textrm {SU}(n, n)$

Abstract:

For each of the two series of groups, three series of representations ${U_n}$, ${D_n}$, and ${H_n}(n \in Z)$ are considered. For each series of representations there is a differential operator with the property, that raised to the nth power $(n > 0)$, it intertwines the representations indexed by $- n$ and n. The operators are generalizations of the d’Alembertian, the Diracoperator and a combination of the two. Unitarity of subquotients of representations indexed by negative integers is derived from the intertwining relations.