Abstract

Let G ⊂ G_C be a connected reductive linear Lie group with a Cartan subgroup B which is compact modulo the center of G. Then G has discrete series representations. Further, since G is linear the characters of discrete series representations can be averaged over the Weyl group to obtain stable discrete series characters which are constant on orbits of G_C in G′, and can be regarded as the restrictions of certain class functions on the regular set G_C′ of G_C. The main theorem of this paper expresses these class functions on G_C′ as “lifts” of analogous class functions on two-structure groups for G_C. These are connected reductive complex Lie groups which are not necessarily subgroups of G_C, but which “share” the Cartan subgroup B_C with G_C. Further, all of their simple factors have root systems of type A₁ or B₂ ≃ C₂.

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