Pré-Publication, Document De Travail Année : 2025

ISOMORPHISMS AMONG QUANTUM GROTHENDIECK RINGS AND CLUSTER ALGEBRAS

Ryo Fujita
  • Fonction : Auteur
Se-Jin Oh
  • Fonction : Auteur
Hironori Oya
  • Fonction : Auteur

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.

Fichier principal
Vignette du fichier
CZisom_general2.pdf (715.91 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04863340 , version 1 (03-01-2025)

Identifiants

Citer

Ryo Fujita, David Hernandez, Se-Jin Oh, Hironori Oya. ISOMORPHISMS AMONG QUANTUM GROTHENDIECK RINGS AND CLUSTER ALGEBRAS. 2025. ⟨hal-04863340⟩
3 Consultations
1 Téléchargements

Altmetric

Partager

More