Strong duality Data of type $A$ and extended $T$-systems

Abstract

The extended $T$-systems are a number of short exact sequences in the category of finite-dimensional modules over the quantum affine algebras of types $A_n^{(1)}$ and $B_n^{(1)}$, 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.

arXiv comment41 pages; corrected the proof of Proposition 4.1.3 (ver. 2); added some examples. This is the final version (ver.3)