A generating function for Blattner's formula

Details A generating function for Blattner's formula A generating function for Blattner's formula

2006-12-11

arxiv.org/abs/math/0612266v2

Mathematics

Representation Theory

12 pages, 4 figures, added section on a positivity result

Scientific paper

Let G be a connected, semisimple Lie group with finite center and let K be a maximal compact subgroup. We investigate a method to compute multiplicities of K-types in the discrete series using a rational expression for a generating function obtained from Blattner's formula. This expression involves a product with a character of an irreducible finite dimensional representation of K and is valid for any discrete series system. Other results include a new proof of a symmetry of Blattner's formula, and a positivity result for certain low rank examples. We consider in detail the situation for G of type split G_2. The motivation for this work came from an attempt to understand pictures coming from Blattner's formula, some of which we include in the paper.

Affiliated with

Also associated with

No associations

Rating

A generating function for Blattner's formula 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 generating function for Blattner's formula, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A generating function for Blattner's formula will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-183589