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For each of the two series of groups, three series of representations      U n {U_n}      ,      D n {D_n}      , and      H n ( n ∈  Z ) {H_n}(n \in Z)       are considered. For each series of representations there is a differential operator with the property, that raised to the  n th power      ( n &gt; 0 ) (n &gt; 0)      , it intertwines the representations indexed by      −  n - 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.

Intertwining differential operators for 𝑀𝑝(𝑛,𝑅) and 𝑆𝑈(𝑛,𝑛)