Unitary highest weight modules for $\mathfrak{su}(p,q)$ and ${\mathfrak{so}}^{\ast }(2n)$ with fixed integral infinitesimal character

Abstract

We classify unitary highest weight modules with a given integral infinitesimal character for the real Lie algebras $\mathfrak{su}(p,q)$ and ${\mathfrak{so}}^{\ast }(2n)$. We treat both regular and singular cases. For $\mathfrak{su}(p,q)$ we identify the unitarizable modules in the Hasse diagrams of the highest weight orbit. Analogous results for the other Hermitian Lie algebras were given in our earlier publications.

31 pages, 4 figures