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Large components of principal series
and characteristic cycles

Author: Jen-Tseh Chang
Journal: Proc. Amer. Math. Soc. 127 (1999), 3367-3373
MSC (1991): Primary 22E46
Published electronically: May 4, 1999
MathSciNet review: 1605932
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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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Additional Information

Jen-Tseh Chang
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078-0613

Received by editor(s): January 22, 1997
Received by editor(s) in revised form: January 21, 1998
Published electronically: May 4, 1999
Additional Notes: We thank J. Cogdell for bringing us into this particular subject, and the referee for helpful suggestions. This research was supported in part by an Arts and Sciences Summer Research grant in 1996 from the Oklahoma State University.
Communicated by: Roe W. Goodman
Article copyright: © Copyright 1999 American Mathematical Society

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