Compact symmetric triads and symmetric triads with multiplicities

2025/06/03 by Baba, Kurando, Ikawa, Osamu
#17B22 #53C35 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.02511

Abstract

In this paper, we develop the theory of symmetric triads with multiplicities. First, we classify abstract symmetric triads with multiplicities. Second, we determine the symmetric triads with multiplicities corresponding to commutative compact symmetric triads. As applications, we give the classifications for commutative compact symmetric triads, which consist of two types depending on the choice of the equivalence relations.

Citations

• Double Satake diagrams and canonical forms in compact symmetric triads
• Geometric Properties of Orbits of Hermann actions
• Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups
• Weakly reflective submanifolds and austere submanifolds
• Calibrated geometries

Related

• Double Satake diagrams and canonical forms in compact symmetric triads
• Fragments in symmetric configurations with block size 3
• Multiplicity-free representations of the symmetric group
• Arithmetic fake compact Hermitian symmetric spaces of Type A₃
• Multi-indicial symmetric functions