International Journal of Mathematics and Mathematical Sciences 
Volume 2005 (2005), Issue 8, Pages 1299-1315
doi:10.1155/IJMMS.2005.1299

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

Alvaro Alvarez-Parrilla

 Facultad de Ciencias, Universidad Autónoma de Baja California, Km. 103 Carretera Tijuana–Ensenada, Apdo. Postal no. 2300, Ensenada, Baja California, Mexico
Received 6 August 2003; Revised 10 March 2005

Abstract

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.