On the classification of unitary highest weight modules in the exceptional cases

Abstract

In our previous paper, we gave a complete classification of the unitary highest weight modules for the universal covers of the Lie groups $Sp(2n,\mathbb{R}),S{O}^{\ast }(2n)$ and $SU(p,q)$, using the Dirac inequality and the so called PRV product. In this paper, we complete the classification of the unitary highest weight modules for the remaining cases; i.e., universal covers of the Lie groups $S{O}_e(2,n)$, $E_{6(-14)}$ and $E_{7(-25)}$. We also describe unitary highest weight modules with given infinitesimal characters.

30 pages

References in corpus (2)

• Dirac inequality for highest weight Harish-Chandra modules II
• Dirac inequality for highest weight Harish-Chandra modules I

Cited by in corpus (1)

• Howe duality for the dual pair $S{L}_2(\mathbb{R})\times F_{4,1}$: a ping-pong of $K$-types