  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).
