On classifying unitary modules by their Dirac cohomology

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

Science China Mathematics, November 2017, Volume 60, Issue 11, pp 1937–1962.

https://doi.org/10.1007/s11425-017-9097-8

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.

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