Journal d’Analyse Mathématique

, Volume 98, Issue 1, pp 249–277 | Cite as

The Power Matrix, coadjoint action and quadratic differentials

  • Eric Schippers


The coefficients of a quadratic differential which is changing under the Loewner flow satisfy a well-known differential system studied by Schiffer, Schaeffer and Spencer, and others. By work of Roth, this differential system can be interpreted as Hamilton's equations. We apply the power matrix to interpret this differential system in terms of the coadjoint action of the matrix group on the dual of its Lie algebra. As an application, we derive a set of integral invariants of Hamilton's equations which is in a certain sense complete. In function theoretic terms, these are expressions in the coefficients of the quadratic differential and Loewner map which are independent of the parameter in the Loewner flow.


Matrix Model Differential System Quadratic Differential Cotangent Bundle Power Matrix 
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Copyright information

© The Hebrew University Magnes Press 2006

Authors and Affiliations

  • Eric Schippers
    • 1
  1. 1.Department of Mathematics Machray HallUniversity of ManitobaWinnipegCanada

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