Classical affine W-algebras and the associated integrable Hamiltonian hierarchies for classical Lie algebras
We prove that any classical affine W-algebra W(g,f), where g is a classical
Lie algebra and f is an arbitrary nilpotent element of g, carries an integrable
Hamiltonian hierarchy of Lax type equations. This is based on the theories of
generalized Adler type operators and of generalized quasideterminants, which we
develop in the paper. Moreover, we show that under certain conditions, the
product of two generalized Adler type operators is a Lax type operator. We use
this fact to construct a large number of integrable Hamiltonian systems,