  Exact critical properties of the one-dimensional SU($N$) interacting fermion
model with open boundaries are studied by using the Bethe ansatz method. We
derive the surface critical exponents of various correlation functions using
boundary conformal field theory. They are classified into two types, i.e. the
exponents for the chiral SU($N$) Tomonaga-Luttinger liquid and those related to
the orthogonality catastrophe. We discuss a possible application of the results
to the photoemission (absorption) in the edge state of the fractional quantum
Hall effect.
