  We revisit the classical Goddard-Kent-Olive coset construction. We find the
formulas for the highest weight vectors in coset decomposition and calculate
their norms. We also derive formulas for matrix elements of natural vertex
operators between these vectors. This leads to relations on conformal blocks.
Due to the AGT correspondence, these relations are equivalent to blowup
relations on Nekrasov partition functions with the presence of the surface
defect. These relations can be used to prove Kyiv formulas for the Painlev\'e
tau-functions (following Nekrasov's method).
