$(q,t)$-characters of Kirillov-Reshetikhin modules of type $A_r$ as quantum cluster variables
| Autor: | Bolor Turmunkh |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Type (model theory)
01 natural sciences Theoretical Computer Science Cluster algebra Combinatorics Quantization (physics) Mathematics::Quantum Algebra 0103 physical sciences Mutation (knot theory) Mathematics - Quantum Algebra Cluster (physics) FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics Quantum Algebra (math.QA) 0101 mathematics Representation Theory (math.RT) Mathematics::Representation Theory Quantum Mathematics Applied Mathematics 010102 general mathematics Quiver Computational Theory and Mathematics Multiplication 010307 mathematical physics Geometry and Topology Combinatorics (math.CO) Mathematics - Representation Theory |
| DOI: | 10.48550/arxiv.1705.10026 |
| Popis: | 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. Comment: 45 pages, 8 figures |
| Databáze: | OpenAIRE |
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