Cluster algebras and quantum affine algebras
By D. Hernandez, Bernard Leclerc. 2009
290 citations recorded by the source corpus.
Let C be the category of finite-dimensional representations of a quantum affine algebra of simply-laced type. We introduce certain monoidal subcategories C_l (l integer) of C and we study their Grothendieck rings using cluster algebras.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/94aee3ad95f6973636375f5b078df5b576856613
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In Discrete Mathematics and Combinatorics
- Pavlo Pylyavskyy
- Masaki Kashiwara
- Sergey Fomin
- H. Nakajima
- Myungho Kim
- Seok-Jin Kang
- Se-jin Oh
- R. Venkatesh
In Geometry and Topology
- D. Hernandez
- Vyjayanthi Chari
- Masaki Kashiwara
- R. Venkatesh
- H. Nakajima
- Pavlo Pylyavskyy
- Myungho Kim
- Se-jin Oh
In Mathematical Physics
- Vyjayanthi Chari
- Pavlo Pylyavskyy
- H. Nakajima
- Sergey Fomin
- Myungho Kim
- Seok-Jin Kang
- Se-jin Oh
- R. Venkatesh
Citations in the corpus
- Simplicity of heads and socles of tensor products (2014, methodology): “On the other hand, the algebra U q (g) is categorified by quiver Hecke algebras ([10, 11, 14]) and also by quantum affine algebras ([4, 5, 7, 8]).”
- Tensor diagrams and cluster algebras (2012, background): “Leclerc’s “reality check” criterion [25,34] according to which the cluster monomials are identified as the real basis elements, i.”
- Demazure Modules, Fusion Products and Q-Systems (2013, background): “These systems have played an important role in the theory of cluster algebras through the work of [24].”