  Let a second order Fuchsian differential equation with only univalued
solutions have finite singular points at z_1, ..., z_n with exponents
(a_1,b_1), ..., (a_n,b_n). Let the exponents at infinity be (A,B). Then for
fixed generic z_1,...,z_n, the number of such Fuchsian equations is equal to
the multiplicity of the irreducible sl_2 representation of dimension |A-B| in
the tensor product of irreducible sl_2 representations of dimensions |a_1-b_1|,
>..., |a_n-b_n|.
  To show this we count the number of critical points of a suitable function
which plays the crucial role in constructions of the hypergeometric solutions
of the sl_2 KZ equation and of the Bethe vectors in the sl_2 Gaudin model. As a
byproduct of this study we conclude that the Bethe vectors form a basis in the
space of states for the sl_2 inhomogeneous Gaudin model.

Quantum Algebra;Classical Analysis and ODEs