Dirac cohomology in representation theory (Q1707325)

To construct the discrete series classified by Harish-Chandra geometrically, Parthasarathy introduced the Dirac operators for semisimple Lie groups in 1972. Later, to understand unitary representations better, Vogan formulated the notion of Dirac cohomology in 1997. After the verification of Vogan's conjecture by Huang and Pandžic in 2002, Dirac cohomology became a new invariant for representations of real reductive Lie groups. Since then, the topic Dirac cohomology attracts ongoing research, and several of its analogues appear in the literature. The paper under review gives a brief introduction to Dirac operators, Dirac cohomology, and to the Huang-Pandžic proof of the Vogan conjecture. Similar to a few other papers of the author, the current one also surveys the developments on this topic (up to the year 2016 or around). For the entire collection see [Zbl 1387.17001].