Geodesic
\((q,t)\)-characters of Kirillov-Reshetikhin modules of type \(A_r\) as quantum cluster variables
Bolor Turmunkh1
1University of Illinois - Urbana Champaign
The electronic journal of combinatorics, Tome 25 (2018) no. 1
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Nakajima (2003) introduced a $t$-deformation of $q$-characters, $(q,t)$-characters for short, and their twisted multiplication through the geometry of quiver varieties. The Nakajima $(q,t)$-characters of Kirillov-Reshetikhin modules satisfy a $t$-deformed $T$-system. The $T$-system is a discrete dynamical system that can be interpreted as a mutation relation in a cluster algebra in two different ways, depending on the choice of direction of evolution. In this paper, we show that the Nakajima $t$-deformed $T$-system of type $A_r$ forms a quantum mutation relation in a quantization of exactly one of the cluster algebra structures attached to the $T$-system.
DOI : 10.37236/7188
Classification : 05E10
Mots-clés : \(T\)-system, quantum cluster algebra, \(q\)-characters

Bolor Turmunkh  1

1 University of Illinois - Urbana Champaign 
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     author = {Bolor Turmunkh},
     title = {\((q,t)\)-characters of {Kirillov-Reshetikhin} modules of type {\(A_r\)} as quantum cluster variables},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {1},
     doi = {10.37236/7188},
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Bolor Turmunkh. \((q,t)\)-characters of Kirillov-Reshetikhin modules of type \(A_r\) as quantum cluster variables. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/7188

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