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arXiv · 2510.10874

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

Se-jin Oh·Travis Scrimshaw
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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.

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Se-jin Oh, Travis Scrimshaw. 2025-10-13. Denominators of R-matrices, higher Dorey's rules and a generalization of T-systems for quantum affine algebras. https://arxiv.org/abs/2510.10874

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