  We study the geometry and partial differential equations arising from the
consideration of group-determinants, and representation theory. The simplest
and most striking such example is undoubtedly that of the Humbert operator,
associated with the cyclic group Z/3Z. This operator appears as a natural
extension of the Laplacian in dimension 2. Another originality of our work is
to show that the spectral theory of operators associated with Frobenius
determinants is closely linked to finite Fourier transform theory.
