  We study a family of modules over Kac-Moody algebras realized in multi-valued
functions on a flag manifold and find integral representations for intertwining
operators acting on these modules. These intertwiners are related to some
expressions involving complex powers of Lie algebra generators.
  When applied to affine Lie algebras, these expressions give integral formulas
for correlation functions with values in not necessarily highest weight
modules.
  We write related formulas out in an explicit form in the case of
$\hat{\gtsl_{2}}$. The latter formulas admit q-deformation producing an
integral representation of q-correlation functions. We also discuss a relation
of complex powers of Lie algebra (quantum group) generators and Casimir
operators to ($q-$)special functions.
