Finite Projective Source Geometry for GL2: Abel Resolvents and Central-Jet Degree Laws
Starting from the two trace functions p1 = Tr(A) and p2 = Tr(A^2) for semisimple A in GL2(C), we develop the associated projective source geometry. The coordinate y = t^2/d - 1 identifies the adjoint character, and normalized Haar measure on a specified closed subgroup H of SO(3) pushes forward to a probability measure nu_H. We describe this measure through harmonic multiplicities, moments, and its Stieltjes transform, and prove that it determines H up to conjugacy within the closed-subgroup class of SO(3). A positive Abel kernel resums the projective character tower and gives a resolvent…
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