Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 49, No. 1, pp. 3357 (2008) 

A geometric embedding for standard analytic modulesTim BrattenFacultad de Ciencias Exactas, UNICEN, Paraje Arroyo Seco, Tandil, Argentina, email: bratten@exa.unicen.edu.arAbstract: In this manuscript we make a general study of the representations realized, for a reductive Lie group of HarishChandra class, on the compactly supported sheaf cohomology groups of an irreducible finiterank polarized homogeneous vector bundle defined in a generalized complex flag space. In particular, we show that the representations obtained are minimal globalizations of HarishChandra 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 qth 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. Full text of the article:
Electronic version published on: 26 Feb 2008. This page was last modified: 28 Jan 2013.
© 2008 Heldermann Verlag
