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arXiv · 1705.10026

$(q,t)$-characters of Kirillov-Reshetikhin modules of type $A_r$ as quantum cluster variables

Bolor Turmunkh
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Abstract

Nakajima 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.

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BibTeXRIS

Bolor Turmunkh. 2017-05-29. $(q,t)$-characters of Kirillov-Reshetikhin modules of type $A_r$ as quantum cluster variables. https://arxiv.org/abs/1705.10026

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