Some geometric facets of the Langlands correspondence for real groups

Rahbar Virk

Published 2013-12-29, updated 2014-09-28Version 3

This note concerns geometric aspects of the local Langlands correspondence for real groups as extended from Langlands' original work by Adams-Barbasch-Vogan, and further (conjectural) formulations by W. Soergel. The main result concerns purity (in the sense of weights in Hodge theory) of equivariant extension groups between simple objects on the Adams-Barbasch-Vogan geometric parameter space (for trivial infinitesimal character).