Dirac series of $GL(n, \mathbb{R})$

Abstract

The unitary dual of GL(n, R) was classified by Vogan in the 1980s. In particular, the Speh representations and the special unipotent representations are the building blocks of the unitary dual with half-integral infinitesimal characters. In this manuscript, we classify all irreducible unitary (g, K)-modules with non-zero Dirac cohomology for GL(n, R), as well as a formula for (one of) their spin-lowest K-types. Moreover, analogous to the GL(n, C) case given in [DW1], we count the number of the FS-scattered representations of GL(n, R).

Dirac series of $E_{7(-5)}$

“…Recently, there has been progresses on the classification of Dirac series. See [2,14]. The current paper is a continuation of this task on exceptional Lie groups.…”