Existence of Kirillov-Reshetikhin crystals for multiplicity-free nodes

DOI10.4171/PRIMS/56-4-4zbMath1454.81111arXiv1902.00769MaRDI QIDQ2216024

Rekha Biswal, Travis Scrimshaw

Publication date: 15 December 2020

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.00769

zbMATH Keywords

crystal basecrystalKirillov-Reshetikhin crystal

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Modular representations and characters (20C20)

Related Items (3)

Kirillov–Reshetikhin crystals B^7,s for type E₇⁽¹⁾ ⋮ Existence of Kirillov-Reshetikhin crystals for near adjoint nodes in exceptional types ⋮ On higher level Kirillov-Reshetikhin crystals, Demazure crystals, and related uniform models

Uses Software

• SageMath
• Sage-Combinat

Cites Work

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• Construction of perfect crystals conjecturally corresponding to Kirillov-Reshetikhin modules over twisted quantum affine algebras
• Existence of crystal bases for Kirillov-Reshetikhin modules of type \(D\)
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Twisted quantum affine algebras
• Virtual crystals and Kleber's algorithm
• Existence of Kirillov-Reshetikhin crystals of type \(G_2^{(1)}\) and \(D_4^{(3)}\)
• On level-zero representation of quantized affine algebras.
• Minimal affinizations of representations of quantum groups: The nonsimply-laced case
• Minimal affinization of representations of quantum groups: The irregular case
• Minimal affinizations of representations of quantum groups: The rank 2 case
• Uniform description of the rigged configuration bijection
• On higher level Kirillov-Reshetikhin crystals, Demazure crystals, and related uniform models
• Perfect crystals for \(U_q(D_4^{(3)})\)
• Crystalizing the q-analogue of universal enveloping algebras
• Kirillov-Reshetikhin Conjecture: The General Case
• Groupes et algébras de Lie
• Proof of the Combinatorial Kirillov-Reshetikhin Conjecture
• Lakshmibai–Seshadri paths of level-zero shape and one-dimensional sums associated to level-zero fundamental representations
• Existence of Kirillov–Reshetikhin crystals for nonexceptional types
• Crystal structure on the set of Lakshmibai-Seshadri paths of an arbitrary level-zero shape

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