A parametrization of K̂ (after Vogan)


Let G be a real reductive group in Harish-Chandra’s class. It may be instructive and useful to weaken that hypothesis, but we content ourselves with it here. Let K be the maximal compact subgroup of G. The point of these notes is to recall a parametrization of K̂ (i.e. equivalence classes of irreducible representations of K) due to David Vogan. Note that even if G is algebraic, the description of K̂ is not covered by Adams’ notes on parameters: the group K need not belong to the class Adams considers (even though the group G does). For orientation one should consult the notes on K̂ compiled last year by David Vogan during the AIM workshop. (These are on the website.) Those notes provide provide a completely different perspective, essentially that of Cartan-Weyl, and parametrize K̂ in terms of irreducible representations of a Cartan subgroup. By contrast, these notes intricately use the fact that our K is the maximal compact subgroup of G.

Cite this paper

@inproceedings{Trapa2004APO, title={A parametrization of K̂ (after Vogan)}, author={Peter Engel Trapa}, year={2004} }