International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 8, Pages 1299-1315

Explicit geodesic flow-invariant distributions using SL2()-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

Copyright © 2005 Alvaro Alvarez-Parrilla. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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(). 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.