A cluster realization of \(U_q(\mathfrak {sl}_{\mathfrak {n}})\) from quantum character varieties

DOI10.1007/s00222-019-00857-6zbMath1451.17006arXiv1607.00271OpenAlexW2909807201MaRDI QIDQ2419709

Gus Schrader, Alexander Shapiro

Publication date: 14 June 2019

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.00271

zbMATH Keywords

quantum groupmapping class group\(R\)-matrixquantum cluster algebracluster mutationquantum dilogarithms

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Cluster algebras (13F60) Character varieties (14M35)

Related Items (13)

On tensor product decomposition of positive representations of \(\mathcal{U}_{q\widetilde{q}}(\mathfrak{sl}(2,\mathbb{R}))\) ⋮ Quantum traces and embeddings of stated skein algebras into quantum tori ⋮ Toda conformal blocks, quantum groups, and flat connections ⋮ Quantum traces for \(\operatorname{SL}_n (\mathbb{C})\): the case \(n = 3\) ⋮ Invariants of Weyl group action and \(q\)-characters of quantum affine algebras ⋮ Multiple generalized cluster structures on ⋮ A Wilson line realization of quantum groups ⋮ Twist automorphisms and Poisson structures ⋮ Positive representations with zero Casimirs ⋮ Cluster realizations of Weyl groups and higher Teichmüller theory ⋮ Quantum Grothendieck rings as quantum cluster algebras ⋮ Fenchel–Nielsen coordinates and Goldman brackets ⋮ Tensor diagrams and cluster combinatorics at punctures

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