Cluster algebras and representation theory

By Bernard Leclerc. 2010

53 citations recorded by the source corpus.

We apply the new theory of cluster algebras of Fomin and Zelevinsky to study some combinatorial problems arising in Lie theory. This is joint work with Geiss and Schr\"oer (3, 4, 5, 6), and with Hernandez (8, 9).

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0129c16733521c4a360ea76953808ce4122837fe

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In Algebra and Number Theory

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Citations in the corpus

Cluster algebras and derived categories (2012, background): “He is very grateful to B. Leclerc for correcting an error in a previous version of example 4.3 and to H. Nakajima for a helpful conversation on the results of [30].”
Total positivity and cluster algebras (2010, background): “Several survey/introductory papers dedicated to the subjects in the title, approached from various perspectives, have already appeared in the literature; see in particular [1, 5, 19, 25, 29, 34, 39, 43, 55, 56, 57].”
Tensor diagrams and cluster algebras (2012, background): “ess a natural structure of a cluster algebra. The list includes homogeneous coordinate rings of partial ﬂag manifolds, Schubert varieties, and double Bruhat cells in semisimple Lie groups; see, e.g., [3,16, 19,29,39]. Of particular importance to us is the example of a Grassmannian Grk,b. As mentione”
Representations of Algebras and Related Topics (2011, unknown): “ case, by using the geometric description of the irreducible q-characters explained in §2. These two diﬀerent proofs will be explained in §3.4 and §3.5. 5We take this opportunity to correct a typo in [30]: in the statement of Conjecture 9.1, one should replace W(i) k,qξi+2(ℓ+1−k) by W(i) k,qξi . Qua”
Cluster categories (2010, methodology): “Another interesting type of categorification was introduced in [70], and pursued in [94], see also [91].”
Ordered Exchange Graphs (2013, background): “More detailed surveys on some of the objects and maps include [105, 63, 31, 78, 90, 66].”