  We introduce Schur multiple zeta functions which interpolate both the
multiple zeta and multiple zeta-star functions of the Euler-Zagier type
combinatorially. We first study their basic properties including a region of
absolute convergence and the case where all variables are the same. Then, under
an assumption on variables, some determinant formulas coming from theory of
Schur functions such as the Jacobi-Trudi, Giambelli and dual Cauchy formula are
established with the help of Macdonald's ninth variation of Schur functions.
Moreover, we investigate the quasi-symmetric functions corresponding to the
Schur multiple zeta functions. We obtain the similar results as above for them
and, furthermore, describe the images of them by the antipode of the Hopf
algebra of quasi-symmetric functions explicitly. Finally, we establish iterated
integral representations of the Schur multiple zeta values of ribbon type,
which yield a duality for them in some cases.
