Affine Grassmannians for triality groups

DOI10.1016/j.jalgebra.2022.05.014zbMath1498.14128arXiv2107.07372OpenAlexW3179422026MaRDI QIDQ2144380

Zhihao Zhao

Publication date: 13 June 2022

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.07372

zbMATH Keywords

trialitycomposition algebrasoctonionsaffine Grassmannians

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Grassmannians, Schubert varieties, flag manifolds (14M15) Loop groups and related constructions, group-theoretic treatment (22E67) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) (14R10) Simple, semisimple, reductive (super)algebras (17B20) Group schemes (14L15)

Cites Work

• Triality and algebraic groups of type \(^3\mathsf D_4\)
• Local models of Shimura varieties and a conjecture of Kottwitz
• Twisted Bhargava cubes
• Topological flatness of orthogonal local models in the split, even case. I
• Twisted loop groups and their affine flag varieties. With an appendix by T. Haines and M. Rapoport.
• Isotopes of octonion algebras, \(\mathbf{G}_{2}\)-torsors and triality
• Integral models of Shimura varieties with parahoric level structure
• On the flatness of local models for the symplectic group.
• An introduction to affine Grassmannians and the geometric Satake equivalence
• On the flatness of models of certain Shimura varieties of PEL-type
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