Lampe, P. (2013) Quantum cluster algebras of type A and the dual canonical basis. Proceedings of the London Mathematical Society, 108 (1). pp. 143. ISSN 00246115. (doi:10.1112/plms/pds098) (KAR id:67634)
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Official URL https://doi.org/10.1112/plms/pds098 
Abstract
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 GeissLeclercSchroeer 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:  https://kar.kent.ac.uk/id/eprint/67634 (The current URI for this page, for reference purposes) 
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