  Dual superconductor picture is one of the most promising scenarios for quark
confinement. We have proposed a new formulation of Yang-Mills theory on the
lattice so that the so-called restricted field obtained from the
gauge-covariant decomposition plays the dominant role in quark confinement.
This framework improves the Abelian projection in the gauge-independent manner.
For quarks in the fundamental representation, we have demonstrated some
numerical evidences for the dual superconductivity. However, it is known that
the expected behavior of the Wilson loop in higher representations cannot be
reproduced if the restricted part of the Wilson loop is extracted by adopting
the Abelian projection or the field decomposition naively in the same way as in
the fundamental representation. In this talk, therefore, we focus on
confinement of quarks in higher representations. By virtue of the non-Abelian
Stokes theorem for the Wilson loop operator, we propose suitable operators
constructed from the restricted field only in the fundamental representation to
reproduce the correct behavior of the original Wilson loop in higher
representations. Moreover, we perform lattice simulations to measure the static
potential for quarks in higher representations using the proposed operators. We
find that the proposed operators well reproduce the expected behavior of the
original Wilson loop average, which overcomes the problem that occurs in
naively applying Abelian-projection to the Wilson loop operator for higher
representations.
