Algebraic Dirac induction for nonholomorphic discrete series of \(\mathrm{SU}(2,1)\) (Q2827857)

Based on the algebraic Dirac induction method introduced in [\textit{P. Pandžić} and \textit{D. Renard}, J. Lie Theory 20, No. 4, 617--641 (2010; Zbl 1211.22010)], the author constructs the nonholomorphic discrete series of \(\mathrm{SU}(2, 1)\) from their Dirac cohomology. We refer the reader to page 894 of the author's paper for the precise meaning of nonholomorphic discrete series. The main result is exhibited in Theorem 5.7, which is achieved by explicitly demonstrating suitable bases for \(\mathcal{A}\otimes W\) and \(X\otimes S\). Here \(X\) is a nonholomorphic discrete series of \(\mathrm{SU}(2,1)\), and \(W\) is its Dirac cohomology.