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Explicit geodesic flow-invariant distributions using SL 2 ( â„ ) -representation ladders

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  • Alvaro Alvarez-Parrilla

Abstract

An explicit construction of a geodesic flow-invariant distribution lying in the discrete series of weight 2 k isotopic component is found, using techniques from representation theory of SL 2 ( â„ ) . 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.

Suggested Citation

  • Alvaro Alvarez-Parrilla, 2005. "Explicit geodesic flow-invariant distributions using SL 2 ( â„ ) -representation ladders," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-17, January.
    • Handle: RePEc:hin:jijmms:401671
    DOI: 10.1155/IJMMS.2005.1299
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