New determinant formulas of Giambelli-type for Schur multiple zeta-functions and their applications

Abstract: In this article, we will prove the Giambelli formula for Schur multiple zeta-functions of extended shape which we call laced type, using the combinatorial method of proving the Giambelli formula for Schur function by Egecioglu and Remmel. Further we will obtain the Giambelli formula for Schur multiple zeta-functions of a certain skew type via the antipode on the set of quasi-symmetric functions. Combining these two Giambelli-type formulas, we will have new identities among Schur multiple zeta-functions.