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

2025/10/13 by Oh, Se-jin, Scrimshaw, Travis
#16T25 #17B37 #17B65 #81R50 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2510.10874

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 \mathfrakd-invariants in monoidal categories over quantum affine algebras and quiver Hecke algebras.

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