  For a quantized enveloping algebra of a complex semisimple Lie algebra with
deformation parameter not a root of unity, we classify all homogeneous right
coideal subalgebras. Any such right coideal subalgebra is determined uniquely
by a triple consisting of two elements of the Weyl group and a subset of the
set of simple roots satisfying some natural conditions. The essential
ingredients of the proof are the Lusztig automorphisms and the classification
of homogeneous right coideal subalgebras of the Borel Hopf subalgebras of
quantized enveloping algebras obtained previously by H.-J. Schneider and the
first named author.
  Key words: Quantum groups, coideal subalgebras, Weyl group, weak order
