Harmonic Analysis in One-Parameter Metabelian Nilmanifolds

Details Harmonic Analysis in One-Parameter Metabelian Nilmanifolds Harmonic Analysis in One-Parameter Metabelian Nilmanifolds

2011-02-27

arxiv.org/abs/1102.5479v1

SIGMA 7 (2011), 021, 16 pages

Mathematics

Group Theory

Scientific paper

10.3842/SIGMA.2011.021

Let $G$ be a connected, simply connected one-parameter metabelian nilpotent Lie group, that means, the corresponding Lie algebra has a one-codimensional abelian subalgebra. In this article we show that $G$ contains a discrete cocompact subgroup. Given a discrete cocompact subgroup $\Gamma$ of $G$, we define the quasi-regular representation $\tau = {\rm ind}_\Gamma^G 1$ of $G$. The basic problem considered in this paper concerns the decomposition of $\tau$ into irreducibles. We give an orbital description of the spectrum, the multiplicity function and we construct an explicit intertwining operator between $\tau$ and its desintegration without considering multiplicities. Finally, unlike the Moore inductive algorithm for multiplicities on nilmanifolds, we carry out here a direct computation to get the multiplicity formula.

Affiliated with

Also associated with

No associations

Rating

Harmonic Analysis in One-Parameter Metabelian Nilmanifolds 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 Harmonic Analysis in One-Parameter Metabelian Nilmanifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Harmonic Analysis in One-Parameter Metabelian Nilmanifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-53920