  We propose a method to generate entanglement measures systematically by using
the irreducible decomposition of some copies of a state under the local unitary
(LU) transformations. It is applicable to general multipartite systems. We show
that there are entanglement monotones corresponding to singlet representations
of the LU group. They can be evaluated efficiently in an algebraic way, and
experimentally measurable by local projective measurements of the copies of the
state. Non-singlet representations are also shown to be useful to classify
entanglement. Our method reproduces many well-known measures in a unified way,
and produces also a lot of new ones.
