Strong Duality Data of Type A and Extended T-Systems

Abstract The extended T -systems are a number of relations in the Grothendieck ring of the category of finite-dimensional modules over the quantum affine algebras of types Aₙ^ (1) A n (1) and Bₙ^ (1) B n (1), introduced by Mukhin and Young as a generalization of the T -systems. In this paper we establish the extended T -systems for more general modules, which are constructed from an arbitrary strong duality datum of type A. Our approach does not use the theory of q -characters, and so also provides a new proof to the original Mukhin–Young’s extended T -systems.