Existence of Kirillov-Reshetikhin crystals for near adjoint nodes in exceptional types

DOI10.1016/j.jpaa.2020.106593zbMath1480.17019arXiv1903.11681OpenAlexW2974260270MaRDI QIDQ2223369

Travis Scrimshaw, Katsuyuki Naoi

Publication date: 28 January 2021

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.11681

zbMATH Keywords

Kirillov-Reshetikhin crystalaffine quantum groupcrystal pseudobase

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Infinite-dimensional Lie (super)algebras (17B65)

Related Items

Kirillov–Reshetikhin crystals B^7,s for type E₇⁽¹⁾ ⋮ A combinatorial realization of Kirillov-Reshetikhin crystals for type E arising from translations

Uses Software

• SageMath

Cites Work

• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Perfect crystals of quantum affine Lie algebras
• Crystal bases of modified quantized enveloping algebra
• Existence of Kirillov-Reshetikhin crystals of type \(G_2^{(1)}\) and \(D_4^{(3)}\)
• On level-zero representation of quantized affine algebras.
• Uniform description of the rigged configuration bijection
• Existence of Kirillov-Reshetikhin crystals for multiplicity-free nodes
• Kirillov-Reshetikhin Conjecture: The General Case
• The Kirillov-Reshetikhin conjecture and solutions of T-systems
• Finite Dimensional Hopf Algebras Arising From Quantized Universal Enveloping Algebras
• Proof of the Combinatorial Kirillov-Reshetikhin Conjecture
• Existence of Kirillov–Reshetikhin crystals for nonexceptional types
• Canonical bases in tensor products.
• Introduction to quantum groups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item