On the discretely decomposable restrictions of (𝔤,K)-modules for Klein four symmetric pairs

DOI10.1142/S0129167X2250094XOpenAlexW4311358070MaRDI QIDQ5879581

Haian He, Yilian Chen

Publication date: 2 March 2023

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129167x2250094x

zbMATH Keywords

reductive Lie groupdiscretely decomposable restrictionKlein four symmetric pair\((\mathfrak{g},K)\)-module

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Cites Work

• Unnamed Item
• Klein four-subgroups of Lie algebra automorphisms
• Elementary abelian 2-subgroups of compact Lie groups
• Classification of discretely decomposable \(A_{\mathfrak q}(\lambda)\) with respect to reductive symmetric pairs
• Discrete decomposability of the restriction of \(A_q(\lambda)\) with respect to reductive subgroups. II: Micro-local analysis and asymptotic \(K\)-support
• Discrete decomposability of restriction of \(A_{\mathfrak q}(\lambda)\) with respect to reductive subgroups and its applications
• Discrete decomposability of the restriction of \(A_{{\mathfrak q}}(\lambda)\) with respect to reductive subgroups. III: Restriction of Harish-Chandra modules and associated varieties
• Classification of Klein four symmetric pairs of holomorphic type for \(\mathrm{E}_{6(-14)}\)
• Classification of Klein four symmetric pairs of holomorphic type for \(\text{E}_{7(-25)}\)
• Classification of symmetric pairs with discretely decomposable restrictions of \((\mathfrak{g},K)\)-modules
• Discretely decomposable restrictions of (𝔤,K)-modules for Klein four symmetric pairs of exceptional Lie groups of Hermitian type
• A criterion for discrete branching laws for Klein four symmetric pairs and its application to E6(−14)
• A necessary condition for discrete branching laws for Klein four symmetric pairs

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