The branching problem for generalized Verma modules, with application to the pair (so(7), LieG2)

DOI10.1142/S0219498814500340zbMath1304.22017arXiv1209.3970WikidataQ115245666 ScholiaQ115245666MaRDI QIDQ2874698

Todor Milev, Petr Somberg

Publication date: 8 August 2014

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.3970

zbMATH Keywords

singular vectorsgeneralized Verma modulescharacter formulasbranching problems\((so(7), \operatorname{Lie}G_{2})\)non-symmetric pairs

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Universal enveloping (super)algebras (17B35) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Cites Work

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• Constructing semisimple subalgebras of semisimple Lie algebras
• Restrictions of generalized Verma modules to symmetric pairs
• A branching law for \(Spin(7,{\mathbb{C}})\to G_ 2\) and its applications to unipotent representations
• Cones, crystals, and patterns
• A generalization of the Bernstein-Gelfand-Gelfand resolution
• The homomorphisms between scalar generalized Verma modules associated to maximal parabolic subalgebras
• Volume computation for polytopes and partition functions for classical root systems
• Canonical factorization of continuous operator functions relative to the circle
• Casimir operators of the exceptional group G2

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