  We consider effects of symmetries on renormalization properties of the
collinear effective theory. We investigate which types of operators are
possible in the effective theory satisfying gauge invariance,
reparameterization invariance and residual energy invariance. Each symmetry
puts a constraint on the possible structure of the theory, and there can appear
only specific combinations of operators in the effective Lagrangian satisfying
all the symmetry requirements. And the final effective Lagrangian is not
renormalized to all orders in alpha_s as long as no other nonlocal operators
are induced at higher order. We explicitly prove this at one loop by
renormalizing one-gluon vertices and discuss their features.
