Cluster algebra structures on module categories over quantum affine algebras

DOI10.1112/plms.12428zbMath1530.81106arXiv1904.01264OpenAlexW2933834118MaRDI QIDQ6134577

Myungho Kim, Masaki Kashiwara, Euiyong Park, Se-jin Oh

Publication date: 22 August 2023

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.01264

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Representations of quivers and partially ordered sets (16G20) Structure, classification theorems for modules and ideals in commutative rings (13C05) Closed categories (closed monoidal and Cartesian closed categories, etc.) (18D15) General theory for finite permutation groups (20B05) Grothendieck groups, (K)-theory and commutative rings (13D15) Cluster algebras (13F60)

Cites Work

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• A cluster algebra approach to \(q\)-characters of Kirillov-Reshetikhin modules
• Quantum unipotent subgroup and dual canonical basis
• Extended T-systems
• Quiver varieties and cluster algebras
• Representations of Khovanov-Lauda-Rouquier algebras and combinatorics of Lyndon words.
• Categorification of highest weight modules via Khovanov-Lauda-Rouquier algebras
• Baxter's relations and spectra of quantum integrable models
• The denominators of normalized \(R\)-matrices of types \(A_{2n-1}^{(2)}\), \(A_{2n}^{(2)}\), \(B_{n}^{(1)}\) and \(D_{n+1}^{(2)}\)
• Homogeneous representations of Khovanov-Lauda algebras.
• Cluster algebras and quantum affine algebras
• Periodicity of Y-systems and flat connections
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras.
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Global crystal bases of quantum groups
• Perfect crystals of quantum affine Lie algebras
• Finite-dimensional representations of quantum affine algebras
• Twisted quantum affine algebras
• Perfect crystals of \(U_q(G_2^{(1)})\)
• On commutation classes of reduced words in Weyl groups
• \(Y\)-systems and generalized associahedra
• Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras
• Monoidal categories associated with strata of flag manifolds
• Quantum Grothendieck ring isomorphisms, cluster algebras and Kazhdan-Lusztig algorithm
• Cluster algebras. III: Upper bounds and double Bruhat cells.
• On level-zero representation of quantized affine algebras.
• Kac-Moody groups, their flag varieties and representation theory
• The periodicity conjecture for pairs of Dynkin diagrams
• Periodicities of T-systems and Y-systems, dilogarithm identities, and cluster algebras. I: Type \(B_r\)
• Periodicities of T-systems and Y-systems, dilogarithm identities, and cluster algebras. II: Types \(C_r, F_4\), and \(G_2\)
• Cluster structures on quantum coordinate rings
• Quantum periodicity and Kirillov-Reshetikhin modules
• Symmetric quiver Hecke algebras and \(R\)-matrices of quantum affine algebras. II
• Triangular bases in quantum cluster algebras and monoidal categorification conjectures
• Categorical relations between Langlands dual quantum affine algebras: exceptional cases
• Perfect crystals for \(U_q(D_4^{(3)})\)
• Quantum cluster algebras.
• CALCULATION OF EXCITATION SPECTRA OF THE SPIN MODEL RELATED WITH THE VECTOR REPRESENTATION OF THE QUANTIZED AFFINE ALGEBRA OF TYPE $A_n^{(1)} $
• FUNCTIONAL RELATIONS IN SOLVABLE LATTICE MODELS I: FUNCTIONAL RELATIONS AND REPRESENTATION THEORY
• Cluster algebras I: Foundations
• Monoidal Categorifications of Cluster Algebras of Type A and D
• Cluster algebras: an introduction
• Quiver Hecke Algebras and 2-Lie Algebras
• Symmetric quiver Hecke algebras andR-matrices of quantum affine algebras III: Table 1.
• A diagrammatic approach to categorification of quantum groups II
• Cluster algebras, quiver representations and triangulated categories
• Canonical bases and KLR-algebras
• Monoidal categorification of cluster algebras
• Kirillov-Reshetikhin Conjecture: The General Case
• The Kirillov-Reshetikhin conjecture and solutions of T-systems
• A diagrammatic approach to categorification of quantum groups I
• Monoidal categories of modules over quantum affine algebras of type A and B
• Simplicity of heads and socles of tensor products
• Laurent phenomenon and simple modules of quiver Hecke algebras
• Cluster algebras of infinite rank