On AGT relation in the case of U (3)

We consider the AGT relation (Alday et al., 2009 [1]), expressing conformal blocks for the Virasoro and W-algebras in terms of Nekrasov's special functions, in the simplest case of the 4-point functions for the first non-trivial W-3 algebra. The standard set of Nekrasov functions is sufficient only if additional null-vector restriction is imposed on a half of the external W-primaries and this is just the case when the conformal blocks are fully dictated by W-symmetry and do not depend on a particular model. Explicit checks confirm that the AGT relation survives in this restricted case, as expected. (C) 2009 Elsevier B.V. All rights reserved.