Discrete Series for Loop Groups.I. An algebraic Realization of Standard Modules

Details Discrete Series for Loop Groups.I. An algebraic Realization of Standard Modules Discrete Series for Loop Groups.I. An algebraic Realization of Standard Modules

1998-09-23

arxiv.org/abs/math/9809131v1

Mathematics

Representation Theory

16 pages, LaTeX2e file, This paper is a revised version of 92-015(1992),IV.1-IV.16, SFB 343, Uni Bielefeld

Scientific paper

In this paper we consider the category $C (\tilde k, \tilde H)$ of the $(\tilde k, \tilde H)$-modules, including all the Verma modules, where $k$ is some compact Lie algebra and H some Cartan subgroup, $\tilde k$ and $\tilde H$ are the corresponding affine Lie algebra and the affine Cartan group, respectively. To this category we apply the Zuckerman functor and its derivatives. By using the determinant bundle structure, we prove the natural duality of the Zuckerman derived functors, and deduce a Borel-Weil-Bott type theorem on decomposition of the nilpotent part cohomology.

Affiliated with

Also associated with

No associations

Rating

Discrete Series for Loop Groups.I. An algebraic Realization of Standard 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 Discrete Series for Loop Groups.I. An algebraic Realization of Standard Modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discrete Series for Loop Groups.I. An algebraic Realization of Standard Modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-194497