  Quasinormal modes of usual, four dimensional, Kerr black holes are described
by certain solutions of a confluent Heun differential equation. In this work,
we express these solutions in terms of the connection matrices for a
Riemann-Hilbert problem, which was recently solved in terms of the Painlev\'e V
transcendent. We use this formulation to generate the small-frequency expansion
for the angular spheroidal harmonic eigenvalue, and derive conditions on the
monodromy properties for the radial modes. Using exponentiation, we relate the
accessory parameter to a semi-classical conformal description and discuss the
properties of the operators involved. For the radial equation, while the
operators at the horizons have Liouville momenta proportional to the entropy
intake, we find that spatial infinity is described by a Whittaker operator.
