Young wall realizations of level 1 irreducible highest weight and Fock space crystals of quantum affine algebras in type E

2023/11/07 by Duncan Laurie, Laurie, Duncan
Mathematics · Physics and Astronomy · #05E10 #17B37 #20G42 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2311.03905

openalex publication_date 2023/11/07 · openalex created_date 2023/11/09 · openalex updated_date 2026/07/28

Abstract

We construct Young wall models for the crystal bases of level 1 irreducible highest weight representations and Fock space representations of quantum affine algebras in types E₆⁽¹⁾, E₇⁽¹⁾ and E₈⁽¹⁾. In each case, Young walls consist of coloured blocks stacked inside the relevant Young wall pattern which satisfy a certain combinatorial condition. Moreover the crystal structure is described entirely in terms of adding and removing blocks.

Related

• Young wall models for the level 1 highest weight and Fock space crystals of U_q(E₆⁽²⁾) and U_q(F₄⁽¹⁾)
• Higher level affine crystals and Young walls
• A new Young wall realization of B(λ) and B(∞)
• Crystal bases for quantum affine algebras and combinatorics of Young walls
• Crystal graphs for basic representations of the quantum affine algebra U_q(C₂⁽¹⁾)