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

On Schur multiple zeta functions: A combinatoric generalization of multiple zeta functions