A Lightcone Embedding of the Twin Building of a Hyperbolic Kac-Moody Group

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Authors: Carbone, Lisa, Feingold, Alex J., Freyn, Walter
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210705
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A Lightcone Embedding of the Twin Building of a Hyperbolic Kac-Moody Group. Lisa Carbone, Alex J. Feingold and Walter Freyn. SIGMA 16 (2020), 045, 47 pages

Let A be a symmetrizable hyperbolic generalized Cartan matrix with Kac-Moody algebra 𝖌 = 𝖌(A) and (adjoint) Kac-Moody group 𝐺 = 𝐺(A) = ⟨exp(ad(teᵢ)),exp(ad(tfᵢ)) | t ∈ ℂ⟩ where ei and fi are the simple root vectors. Let (B⁺, B⁻, N) be the twin BN-pair naturally associated to 𝐺 and let (𝓑⁺, 𝓑⁻) be th...