  A hierarchy of pairwise commuting Hamiltonians for the quantum periodic
Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors
of these Hamiltonians are Jack symmetric functions of infinitely many variables
$x_1,x_2,\ldots$. This construction provides explicit expressions for the
Hamiltonians in terms of the power sum symmetric functions
$p_n=x_1^n+x_2^n+\cdots$ and is based on our recent results from [Comm. Math.
Phys. 324 (2013), 831-849, arXiv:1212.2781].
