التفاصيل البيبلوغرافية
| العنوان: |
Monoidal categorification and quantum affine algebras II. |
| المؤلفون: |
Kashiwara, Masaki, Kim, Myungho, Oh, Se-jin, Park, Euiyong |
| المصدر: |
Inventiones Mathematicae; May2024, Vol. 236 Issue 2, p837-924, 88p |
| مصطلحات موضوعية: |
CLUSTER algebras, AFFINE algebraic groups, ALGEBRA |
| مستخلص: |
We introduce a new family of real simple modules over the quantum affine algebras, called the affine determinantial modules, which contains the Kirillov-Reshetikhin (KR)-modules as a special subfamily, and then prove T-systems among them which generalize the T-systems among KR-modules and unipotent quantum minors in the quantum unipotent coordinate algebras simultaneously. We develop new combinatorial tools: admissible chains of i -boxes which produce commuting families of affine determinantial modules, and box moves which describe the T-system in a combinatorial way. Using these results, we prove that various module categories over the quantum affine algebras provide monoidal categorifications of cluster algebras. As special cases, Hernandez-Leclerc categories C g 0 and C g − provide monoidal categorifications of the cluster algebras for an arbitrary quantum affine algebra. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
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