On classifying unitary modules by their Dirac cohomology

Authors:  Jing-Song Huang, Pavle Pandžić, David Vogan

Science China MathematicsVolume 60, Issue 11pp 1937–1962.


Abstract: Let G be a connected real reductive group with maximal compact subgroup K of the same rank as G. Dirac cohomology of an A_{\mathfrak{q}}(\lambda) module can be identified with a geometric object—the \mathfrak{t}-dominant part of a face of the convex hull of the Weyl group orbit of the parameter \lambda + \rho. We show how Dirac cohomology can be used as a parameter to classify the  A_{\mathfrak q}(\lambda) modules.