Large components of principal series and characteristic cycles

Chang, Jen-Tseh

doi:10.1090/S0002-9939-99-04869-8

Large components of principal series and characteristic cycles
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Proc. Amer. Math. Soc. 127 (1999), 3367-3373 Request permission

Abstract:

For a semisimple quasi-split real linear group which is also maximal in Kostant’s sense, a theorem of Vogan asserts that there is a unique composition factor that is large in any principal series. We give a proof of this theorem using results of Schmid and Vilonen that establish a conjecture of Barbasch and Vogan about characteristic cycles. As a byproduct, we obtain some information about the characteristic cycles of the localized $K$-equivariant sheaves of these principal series.

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