Proving dualities for qMZVs with connected sums

Abstract

This paper gives a new application of so-called connected sums, introduced recently by Seki and Yamamoto. 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 relations, a generalization of Bradley-Zhao duality, is also obtained.