Lax operator
The algebra
was essentially guessed. But it turns out that it has a natural interpretation
in the string worldsheet theory.

Lax pair
For the pure spinor superstring in
the Lax pair was constructed by
B.C.Vallilo:

where
are generators of
:




and
is a complex number which is called spectral parameter.

It follows from the equations of motion that . This observation
can be taken as a starting point of the classical integrability theory.
We will now discuss generalizations of this construction.