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We prove the Pieri formulas for Schur multiple zeta functions, which aregeneralizations of the Pieri formulas proved by Nakasuji and Takeda for hooktype Schur multiple zeta functions. Moreover, we also prove theLittlewood-Richardson rule for Schur multiple zeta functions. In the course oftheir proofs, we regard the `truncated' version of Schur multiple zetafunctions as series over $\mathrm{GL}(N)$ crystals to arrive at theLittlewood-Richardson rule for the Schur multiple zeta functions.

The Pieri formulas and the Littlewood-Richardson rule for Schur multiple zeta functions