Rigged configurations and the ⁎-involution for generalized Kac–Moody algebras

2018/12/31 by Ben Salisbury, Travis Scrimshaw · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Biology #Combinatorics #Involution (esoterism) #Lambda #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #math.CO #math.QA #math.RT #msc:05E10 #msc:17B37

paper · pdf · doi:10.1016/j.jalgebra.2020.12.035

published in Journal of Algebra 573, 148-168 (Elsevier BV) · 18 pages, 1 figure; v2, removed Section 7 since there was an error in our proof of Theorem 7.4, added isotropic imaginary roots case

openalex created_date 2018/12/22 · arxiv created 2020/06/06 · openalex publication_date 2021/01/14 · arxiv updated 2021/01/25 · openalex updated_date 2026/08/05

Abstract

We construct a uniform model for highest weight crystals and B(∞) for generalized Kac--Moody algebras using rigged configurations. We also show an explicit description of the ∗-involution on rigged configurations for B(∞): that the ∗-involution interchanges the rigging and the corigging. We do this by giving a recognition theorem for B(∞) using the ∗-involution. As a consequence, we also characterize B(λ) as a subcrystal of B(∞) using the ∗-involution.

Citations

• On crystal bases of the Q-analogue of universal enveloping algebras
• Crystal structure on rigged configurations
• Crystalizing theq-analogue of universal enveloping algebras
• Monstrous moonshine and monstrous Lie superalgebras
• Rigged Configurations for all Symmetrizable Types
• Monstrous Moonshine
• Canonical Bases Arising from Quantized Enveloping Algebras