We study sl2 and sl3 global conformal blocks on a sphere and a torus, using the shadow formalism. These blocks arise in the context of Virasoro and W3
Nearby in the stack
conformal field theories in the large central charge limit. In the
sl2
case, we demonstrate that the shadow formalism yields the known expressions in terms of conformal partial waves. Then, we extend this approach to the
sl3
case and show that it allows to build simple integral representations for
sl3
global blocks. We demonstrate this construction on two examples: the four-point block on the sphere and the one-point torus block.