Generic bases for cluster algebras and the Chamber Ansatz
From MaRDI portal
Publication:3115807
DOI10.1090/S0894-0347-2011-00715-7zbMath1236.13020arXiv1004.2781MaRDI QIDQ3115807
Bernard Leclerc, Christof Geiss, Jan Schröer
Publication date: 11 February 2012
Published in: Journal of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1004.2781
Grassmannians, Schubert varieties, flag manifolds (14M15) Representations of quivers and partially ordered sets (16G20) Kac-Moody groups (20G44) Cluster algebras (13F60)
Related Items
Cluster characters and the combinatorics of Toda systems, On a family of Caldero-Chapoton algebras that have the Laurent phenomenon, The existence of greedy bases in rank 2 quantum cluster algebras, Tensor diagrams and cluster algebras, Twists of Plücker coordinates as dimer partition functions, POSITIVITY FOR REGULAR CLUSTER CHARACTERS IN ACYCLIC CLUSTER ALGEBRAS, Toda systems, cluster characters, and spectral networks, Quantum twist maps and dual canonical bases, Bases for cluster algebras from orbifolds, Cluster algebras of type \(A\) \(_{{2}}^{{(1)}}\), The Chamber Ansatz for quantum unipotent cells, A quantum analogue of generic bases for affine cluster algebras., Cluster scattering diagrams and theta functions for reciprocal generalized cluster algebras, Wilson lines and their Laurent positivity, Cluster scattering diagrams and theta basis for reciprocal generalized cluster algebras, Perfect bases in representation theory: three mountains and their springs, Perfect matching modules, dimer partition functions and cluster characters, The multiplication formulas of weighted quantum cluster functions, Twist automorphisms and Poisson structures, Quantum unipotent subgroup and dual canonical basis, Cluster algebras in algebraic Lie theory, Integral bases of cluster algebras and representations of tame quivers., Cluster ensembles and Kac-Moody groups, Bricks over preprojective algebras and join-irreducible elements in Coxeter groups, Positivity for generalized cluster variables of affine quivers, Bases for cluster algebras from surfaces, Bases of the quantum cluster algebra of the Kronecker quiver., On cluster algebras with coefficients and 2-Calabi-Yau categories, Book Review: Lecture notes on cluster algebras, A survey on maximal green sequences, Quantum cluster characters of Hall algebras, Schemes of modules over gentle algebras and laminations of surfaces, Compare triangular bases of acyclic quantum cluster algebras, Cluster theory of the coherent Satake category, Cluster Characters, Caldero-Chapoton algebras, Linear independence of cluster monomials for skew-symmetric cluster algebras, On Jacobian algebras associated with the once-punctured torus
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Generic variables in acyclic cluster algebras
- Derived equivalences from mutations of quivers with potential
- The ubiquity of generalized cluster categories
- Kac-Moody groups and cluster algebras
- Cluster categories for algebras of global dimension 2 and quivers with potential.
- Cluster-tilted algebras are Gorenstein and stably Calabi-Yau
- Partial flag varieties and preprojective algebras.
- Cluster characters for 2-Calabi-Yau triangulated categories.
- Quivers with potentials and their representations. I: Mutations.
- Total positivity in Schubert varieties
- Minimal singularities for representations of Dynkin quivers
- Kac-Moody groups, their flag varieties and representation theory
- Parametrizations of canonical bases and totally positive matrices
- From triangulated categories to cluster algebras
- Cluster algebras as Hall algebras of quiver representations.
- Rigid modules over preprojective algebras.
- Cluster algebras I: Foundations
- Mutation of cluster-tilting objects and potentials
- Cluster structures for 2-Calabi–Yau categories and unipotent groups
- Cluster algebras IV: Coefficients
- Quivers with potentials and their representations II: Applications to cluster algebras
- Quivers, Perverse Sheaves, and Quantized Enveloping Algebras
- On the exceptional fibres of Kleinian singularities
- Irreducible components of varieties of modules
- On cluster algebras with coefficients and 2-Calabi-Yau categories
- Semicanonical bases and preprojective algebras