Diagrams for varieties of minimal rational tangents on the wonderful symmetric varieties

2023/06/17 by Shin-young Kim, Kim, Shin-young
Mathematics · Physics and Astronomy · #14H10 #14M27 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2306.10242

openalex publication_date 2023/06/17 · openalex created_date 2023/06/22 · openalex updated_date 2026/07/28

Abstract

We describe varieties of minimal rational tangents on the wonderful symmetric varieties by marked Dynkin diagrams. An irreducible component of a variety of minimal rational tangents is a rational homogeneous space, and hence, we have a corresponding marked Dynkin diagram expression. On the other hand, we have marked Dynkin diagrams from the marked Kac diagram of a irreducible symmetric space by marking adjacent nodes to the marked node. We note that the above two diagrams coincide when the restricted root system is not of type A.

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