  We introduce real Loesungen as an analogue of real roots. For each mutation
sequence of an arbitrary skew-symmetrizable matrix, we define a family of
reflections along with associated vectors which are real Loesungen and a set of
curves on a Riemann surface. The matrix consisting of these vectors is called
L-matrix. We explain how the L-matrix naturally arises in connection with the
C-matrix. Then we conjecture that the L-matrix depends (up to signs of row
vectors) only on the seed, and that the curves can be drawn without
self-intersections, providing a new combinatorial/geometric description of
c-vectors.
