ISOMORPHISMS AMONG QUANTUM GROTHENDIECK RINGS AND CLUSTER ALGEBRAS
Résumé
We establish a cluster theoretical interpretation of the isomorphisms of [FHOO22] among quantum Grothendieck rings of representations of quantum loop algebras. Consequently, we obtain a quantization of the monoidal categorification theorem of [KKOP21b]. We establish applications of these new ingredients. First we solve long-standing problems for any non-simply-laced quantum loop algebras: the positivity of (q, t)-characters of all simple modules, and the analog of Kazhdan-Lusztig conjecture for all reachable modules (in the cluster monoidal categorification). We also establish the conjectural quantum T -systems for the (q, t)-characters of Kirillov-Reshetikhin modules. Eventually, we show that our isomorphisms arise from explicit birational transformations of variables, which we call substitution formulas. This reveals new non-trivial relations among (q, t)-characters of simple modules.
Origine | Fichiers produits par l'(les) auteur(s) |
---|