Let G be a connected reductive
quasi-split algebraic group defined over a p-adic field F of characteristic zero. For π
irreducible admissible generic tempered representation of a standard Levi subgroup
M of G, we prove that the normalized intertwining operators are holomorphic and
nonvanishing on a set larger than the closure of the positive chamber of M,
under some assumptions. As an application, we prove that if G is a split
special orthogonal group (if G is even orthogonal, F can be archimedean)
and π is an irreducible unitary representation of the Siegel Levi subgroup
M of G, then the normalized intertwining operators are holomorphic and
nonvanishing on a set larger than the closure of the positive chamber of
M.
