Non-stationary difference equation for q-Virasoro conformal blocks

Conformal blocks of q, , t-deformed Virasoro and W-algebras are important special functions in representation theory with applications in geometry and physics. In the Nekrasov-Shatashvili limit t -> 1, whenever one of the representations is degenerate then conformal block satisfies a difference equation with respect to the coordinate associated with that degenerate representation. This is a stationary Schrodinger equation for an appropriate relativistic quantum integrable system. It is expected that generalization to generic t (sic) 1 is a non-stationary Schrodinger equation where t parametrizes shift in time. In this paper we make the non-stationary equation explicit for the q, , t- Virasoro block with one degenerate and four generic Verma modules and prove it when three modules out of five are degenerate, using occasional relation to Macdonald polynomials.