The absolute continuous spectrum of skew products of compact Lie groups
Rafael Tiedra de Aldecoa (PUC-Santiago, Chile)

Let X and G be compact Lie groups, F1 : X ! X the time-one map of a C1 measure-preserving flow,  : X ! G a continuous function and  a finite-dimensional irreducible unitary representation of G. Then, we prove that the skew products T : X  G ! X  G; (x; g) 7! ?? F1(x); (x) ; have purely absolutely continuous spectrum in the subspace associated to  if    has a Dinicontinuous Lie derivative along the flow and if a matrix multiplication operator related to the topological degree of    has nonzero determinant. This result provides a simple, but general, criterion for the presence of an absolutely continuous component in the spectrum of skew products of compact Lie groups.
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