quantum cluster algebra
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Author(s):  
Léa Bittmann

AbstractWe establish a quantum cluster algebra structure on the quantum Grothendieck ring of a certain monoidal subcategory of the category of finite-dimensional representations of a simply-laced quantum affine algebra. Moreover, the (q, t)-characters of certain irreducible representations, among which fundamental representations, are obtained as quantum cluster variables. This approach gives a new algorithm to compute these (q, t)-characters. As an application, we prove that the quantum Grothendieck ring of a larger category of representations of the Borel subalgebra of the quantum affine algebra, defined in a previous work as a quantum cluster algebra, contains indeed the well-known quantum Grothendieck ring of the category of finite-dimensional representations. Finally, we display our algorithm on a concrete example.



2020 ◽  
Vol 22 (8) ◽  
pp. 2453-2509 ◽  
Author(s):  
Kenneth Goodearl ◽  
M. T. Yakimov


2019 ◽  
Vol 533 ◽  
pp. 106-141
Author(s):  
Liqian Bai ◽  
Xueqing Chen ◽  
Ming Ding ◽  
Fan Xu


2018 ◽  
Vol 23 (2) ◽  
pp. 391-424 ◽  
Author(s):  
P. DI FRANCESCO ◽  
R. KEDEM




2014 ◽  
Vol 47 (47) ◽  
pp. 474006 ◽  
Author(s):  
Kazuhiro Hikami ◽  
Rei Inoue


2011 ◽  
Vol 28 (6) ◽  
pp. 1169-1178 ◽  
Author(s):  
Ming Ding ◽  
Fan Xu


2011 ◽  
Vol 61 (4) ◽  
pp. 1077-1090 ◽  
Author(s):  
Xueqing Chen ◽  
Ming Ding ◽  
Jie Sheng


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