A Geometric Embedding for Standard Analytic Modules

Details A Geometric Embedding for Standard Analytic Modules A Geometric Embedding for Standard Analytic Modules

2005-03-28

arxiv.org/abs/math/0503646v3

Beitrage zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 49, No. 1, pp. 33-57 (2008)

Mathematics

Representation Theory

21 pages

Scientific paper

In this manuscript we make a general study of the representations realized, for a reductive Lie group of Harish-Chandra class, on the compactly supported sheaf cohomology groups of an irreducible finite-rank polarized homogeneous vector bundle defined in a generalized complex flag space. In particular, we show that the representations obtained are minimal globalizations of Harish-Chandra modules and that there exists a whole number q, depending only on the orbit, such that all cohomologies vanish in degree less than q. The representation realized on the q-th cohomology group is called a standard analytic module. Our main result is a geometric proof that a standard analytic module embeds naturally in an associated standard module defined on the full flag space of Borel subalgebras. As an application, we give geometric realizations for irreducible submodules of some principal series representations in case the group is complex.

Affiliated with

Also associated with

No associations

Rating

A Geometric Embedding for Standard Analytic Modules 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 Geometric Embedding for Standard Analytic Modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Geometric Embedding for Standard Analytic Modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-161677