Explicit geodesic flow-invariant distributions using SL2(ℝ)-representation ladders

Explicit geodesic flow-invariant distributions using SL2(ℝ)-representation ladders

An explicit construction of a geodesic flow-invariant distribution lying in the discrete series of weight 2k isotopic component is found, using techniques from representation theory of SL2(ℝ). It is found that the distribution represents an AC measure on the unit tangent bundle of the hyperbolic pla...

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Main Author: Alvaro Alvarez-Parrilla
Format: Article
Language:English
Published: Hindawi Limited 2005-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/IJMMS.2005.1299
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spelling doaj-0b7550bbcd0a48328b88abe1484ee85a2020-11-25T00:16:09ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-01200581299131510.1155/IJMMS.2005.1299Explicit geodesic flow-invariant distributions using SL2(ℝ)-representation laddersAlvaro Alvarez-Parrilla0Facultad de Ciencias, Universidad Autónoma de Baja California, Km. 103 Carretera Tijuana–Ensenada, Apdo. Postal no. 2300, Ensenada, Baja California, MexicoAn explicit construction of a geodesic flow-invariant distribution lying in the discrete series of weight 2k isotopic component is found, using techniques from representation theory of SL2(ℝ). It is found that the distribution represents an AC measure on the unit tangent bundle of the hyperbolic plane minus an explicit singular set. Finally, via an averaging argument, a geodesic flow-invariant distribution on a closed hyperbolic surface is obtained.http://dx.doi.org/10.1155/IJMMS.2005.1299
collection DOAJ
language English
format Article
sources DOAJ
author Alvaro Alvarez-Parrilla
spellingShingle Alvaro Alvarez-Parrilla
Explicit geodesic flow-invariant distributions using SL2(ℝ)-representation ladders
International Journal of Mathematics and Mathematical Sciences
author_facet Alvaro Alvarez-Parrilla
author_sort Alvaro Alvarez-Parrilla
title Explicit geodesic flow-invariant distributions using SL2(ℝ)-representation ladders
title_short Explicit geodesic flow-invariant distributions using SL2(ℝ)-representation ladders
title_full Explicit geodesic flow-invariant distributions using SL2(ℝ)-representation ladders
title_fullStr Explicit geodesic flow-invariant distributions using SL2(ℝ)-representation ladders
title_full_unstemmed Explicit geodesic flow-invariant distributions using SL2(ℝ)-representation ladders
title_sort explicit geodesic flow-invariant distributions using sl2(ℝ)-representation ladders
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2005-01-01
description An explicit construction of a geodesic flow-invariant distribution lying in the discrete series of weight 2k isotopic component is found, using techniques from representation theory of SL2(ℝ). It is found that the distribution represents an AC measure on the unit tangent bundle of the hyperbolic plane minus an explicit singular set. Finally, via an averaging argument, a geodesic flow-invariant distribution on a closed hyperbolic surface is obtained.
url http://dx.doi.org/10.1155/IJMMS.2005.1299
work_keys_str_mv AT alvaroalvarezparrilla explicitgeodesicflowinvariantdistributionsusingsl2rrepresentationladders
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