A Localization Argument for Characters of Reductive Lie Groups

Details A Localization Argument for Characters of Reductive Lie Groups A Localization Argument for Characters of Reductive Lie Groups

2002-06-04

arxiv.org/abs/math/0206019v4

Mathematics

Representation Theory

43 pages, no figures, to appear in the JFA, some typos removed, final version

Scientific paper

This article provides a geometric bridge between two entirely different character formulas for reductive Lie groups and answers the question posed by W.Schmid in [Sch]. A corresponding problem in the compact group setting was solved by N.Berline, E.Getzler and M.Vergne in [BGV] by an application of the theory of equivariant forms and particularly the fixed point integral localization formula. This article (besides its representation-theoretical significance) provides a whole family of examples where it is possible to localize integrals to fixed points with respect to an action of a NONcompact group. Moreover, a localization argument given here is not specific to the particular setting considered in this article and can be extended to a more general situation. There is a broadly accessible article [L] which explains how the argument works in the SL(2,R) case, where the key ideas are not obstructed by technical details and where it becomes clear how it extends to the general case.

Affiliated with

Also associated with

No associations

Rating

A Localization Argument for Characters of Reductive Lie Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Localization Argument for Characters of Reductive Lie Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Localization Argument for Characters of Reductive Lie Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-96133