Strong Duality Data of Type A and Extended T-Systems

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.