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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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1299 |
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| _version_ | 1832554130512543744 |
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| author | Alvaro Alvarez-Parrilla |
| author_facet | Alvaro Alvarez-Parrilla |
| author_sort | Alvaro Alvarez-Parrilla |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-0b7550bbcd0a48328b88abe1484ee85a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0b7550bbcd0a48328b88abe1484ee85a2025-02-03T05:52:11ZengWileyInternational 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 |
| spellingShingle | Alvaro Alvarez-Parrilla Explicit geodesic flow-invariant distributions using SL2(ℝ)-representation ladders International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | Explicit geodesic flow-invariant distributions using SL2(ℝ)-representation ladders |
| title_sort | explicit geodesic flow invariant distributions using sl2 r representation ladders |
| url | http://dx.doi.org/10.1155/IJMMS.2005.1299 |
| work_keys_str_mv | AT alvaroalvarezparrilla explicitgeodesicflowinvariantdistributionsusingsl2rrepresentationladders |