Reduction of Divisors and the Clebsch System

There are a few Lax matrices of the Clebsch system. Poles of the Baker – Akhiezer function determine the class of equivalent divisors on the corresponding spectral curves. According to the Riemann – Roch theorem, each class has a unique reduced representative. We discuss properties of such a reduced divisor on the spectral curve of $3\times 3$ Lax matrix having a natural generalization to $gl^*(n)$ case.