Denominators of R-matrices, higher Dorey's rules and a generalization of T-systems for quantum affine algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917207036919808 |
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| author | Oh, Se-jin Scrimshaw, Travis |
| author_facet | Oh, Se-jin Scrimshaw, Travis |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_10874 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Denominators of R-matrices, higher Dorey's rules and a generalization of T-systems for quantum affine algebras Oh, Se-jin Scrimshaw, Travis Quantum Algebra 81R50, 17B37, 17B65, 16T25 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. |
| title | Denominators of R-matrices, higher Dorey's rules and a generalization of T-systems for quantum affine algebras |
| topic | Quantum Algebra 81R50, 17B37, 17B65, 16T25 |
| url | https://arxiv.org/abs/2510.10874 |