Denominators of R-matrices, higher Dorey's rules and a generalization of T-systems for quantum affine algebras

Abstract

We construct a higher level analogue of Dorey's rule, which describe certain surjective morphisms between Kirillov--Reshetikhin (KR) modules over quantum affine algebras. Building on this, we establish a generalized T-system of short exact sequences and prove the denominator formula between KR modules in all nonexceptional types, except with only mild ambiguities persisting in type $C_n^{(1)}$. As a consequence, we can completely classify when a tensor product of KR modules is simple. These results have further applications to Schur positivity statements, quiver Hecke algebras, and the recently introduced $\mathfrak{d}$-invariants in monoidal categories over quantum affine algebras and quiver Hecke algebras.

This paper is a thoroughly revised version of our previous work [Simplicity of tensor products of Kirillov Reshetikhin modules; nonexceptional affine and G types] (arXiv 1910.10347). While main results are similar, the proofs are largely new, several earlier conjectures are now proved, and additional new results are obtained. The previous paper is withdrawn