Quantization of virtual Grothendieck rings and their structure including quantum cluster algebras

DOI10.1007/s00220-024-05037-zMaRDI QIDQ6584359

Kyu-Hwan Lee, Se-jin Oh, Il-Seung Jang

Publication date: 6 August 2024

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Mathematics Subject Classification ID

Groups and algebras in quantum theory (81Rxx) Lie algebras and Lie superalgebras (17Bxx) Hopf algebras, quantum groups and related topics (16Txx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A cluster algebra approach to \(q\)-characters of Kirillov-Reshetikhin modules
• Quantum unipotent subgroup and dual canonical basis
• Quiver varieties and cluster algebras
• Derived Hall algebras
• Baxter's relations and spectra of quantum integrable models
• Cluster algebras and quantum affine algebras
• Quantum R matrix for the generalized Toda system
• Kazhdan-Lusztig conjecture and holonomic systems
• Representations of Coxeter groups and Hecke algebras
• Hall algebras and quantum groups
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Quantum affine algebras and holonomic difference equations
• Global crystal bases of quantum groups
• Braid group action and quantum affine algebras
• Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras
• Quantum Grothendieck ring isomorphisms, cluster algebras and Kazhdan-Lusztig algorithm
• Monomials of \(q\) and \(q,t\)-characters for non simply-laced quantum affinizations
• Killing and the Coxeter transformation of Kac-Moody algebras
• Algebraic approach to \(q,t\)-characters
• Cluster structures on quantum coordinate rings
• Quantum Grothendieck rings and derived Hall algebras
• Q-data and representation theory of untwisted quantum affine algebras
• A quantum cluster algebra approach to representations of simply laced quantum affine algebras
• Isomorphisms among quantum Grothendieck rings and propagation of positivity
• Categorical relations between Langlands dual quantum affine algebras: doubly laced types
• Symmetric quiver Hecke algebras and \(R\)-matrices of quantum affine algebras. II
• Quantum cluster algebras.
• Quiver varieties and \(t\)-analogs of \(q\)-characters of quantum affine algebras
• Folded quantum integrable models and deformed \(W\)-algebras
• The \((q, t)\)-Cartan matrix specialized at \(q=1\) and its applications
• Cluster algebras I: Foundations
• A diagrammatic approach to categorification of quantum groups II
• Monoidal categorification of cluster algebras
• The Kirillov-Reshetikhin conjecture and solutions of T-systems
• Canonical Bases Arising from Quantized Enveloping Algebras
• A diagrammatic approach to categorification of quantum groups I
• Powers of Coxeter elements in infinite groups are reduced
• Quiver varieties and finite dimensional representations of quantum affine algebras
• Monoidal categories of modules over quantum affine algebras of type A and B
• Simplicity of heads and socles of tensor products
• Monoidal categorification and quantum affine algebras
• CRYSTAL BASES AND CATEGORIFICATIONS - CHERN MEDAL LECTURE
• Quantum cluster algebra structures on quantum nilpotent algebras
• Deformed Cartan Matrices and Generalized Preprojective Algebras I: Finite Type
• Introduction to quantum groups
• Combinatorics of \(q\)-characters of finite-dimensional representations of quantum affine algebras.
• \(t\)-quantized Cartan matrix and R-matrices for cuspidal modules over quiver Hecke algebras
• Monoidal categorification and quantum affine algebras. II

This page was built for publication: Quantization of virtual Grothendieck rings and their structure including quantum cluster algebras