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Quantum cluster algebras of type A and the dual canonical basis

Lampe, P. (2013) Quantum cluster algebras of type A and the dual canonical basis. Proceedings of the London Mathematical Society, 108 (1). pp. 1-43. ISSN 0024-6115. (doi:10.1112/plms/pds098) (KAR id:67634)

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The article concerns the subalgebra U_v^+(w) of the quantized universal enveloping algebra of the complex Lie algebra sl_{n+1} associated with a particular Weyl group element of length 2n. We verify that U_v^+(w) can be endowed with the structure of a quantum cluster algebra of type A_n. The quantum cluster algebra is a deformation of the ordinary cluster algebra Geiss-Leclerc-Schroeer attached to w using the representation theory of the preprojective algebra. Furthermore, we prove that the quantum cluster variables are, up to a power of v, elements in the dual of Lusztig's canonical basis under Kashiwara's bilinear form.

Item Type: Article
DOI/Identification number: 10.1112/plms/pds098
Subjects: Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Q Science > QA Mathematics (inc Computing science) > QA171 Representation theory
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Philipp Lampe
Date Deposited: 16 Jul 2018 15:58 UTC
Last Modified: 29 May 2019 20:43 UTC
Resource URI: (The current URI for this page, for reference purposes)
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