  Let G be the group of points of a quasi-split reductive algebraic group over
a local field F. It follows from the local Langlands conjectures that to every
non-trivial additive character of F and every representation of the Langlands
dual group of F one can associate certain meromorphic function on the set of
isomorphism classed of irreducible representations of G (which we call
gamma-functions).
  In this paper we describe a general framework for an explicit construction of
these gamma-functions. We make this idea precise in certain special cases. As a
byproduct we give explicit conjectural formulas for the representation
$l_E(\theta)$ of the group GL(n,F) associated to a character $\theta$ of the
multiplicative group $E^*$ of a separable extension E of F of degree n.
  We also describe a conjectural analogue of the Poisson summation formula
associated to a representation of the Langlands dual group, which implies the
existence of the meromorphic continuation and functional equation for the
corresponding automorphic L-functions.
