Proving dualities for $q$MZVs with connected sums

Abstract

This paper gives an application of so-called connected sums, introduced recently by Seki and Yamamoto [SY]. Special about our approach is that it proves a duality for the Schlesinger–Zudilin and the Bradley–Zhao model of qMZVs simultaneously. The latter implies the duality for MZVs and the former can be used to prove the shuffle product formula for MZVs. Furthermore, the $q$-Ohno relation, a generalization of Bradley–Zhao duality, is also obtained.