Characteristic cycles of discrete series for 𝑅-rank one groups

Chang, Jen-Tseh

doi:10.1090/S0002-9947-1994-1145961-2

Characteristic cycles of discrete series for $\textbf {R}$-rank one groups
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Trans. Amer. Math. Soc. 341 (1994), 603-622 Request permission

Abstract:

We determine the characteristic cycles of the discrete series representations for connected $\mathbb {R}$-rank one linear groups. The computation is made through the moment maps; we determine their fibers and the cohomology in question case by case. The multiplicity of the discrete series, in terms of their Harish-Chandra parameters, is given by recursive formulae; for groups of type $A$ and $B$ closed formulae are obtained.

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