A branching law for \(Spin(7,{\mathbb{C}})\to G_ 2\) and its applications to unipotent representations

DOI10.1016/0021-8693(90)90106-XzbMath0701.17003OpenAlexW1983636782MaRDI QIDQ913926

William M. McGovern

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0021-8693(90)90106-x

zbMATH Keywords

unipotent representationexceptional Lie algebrabranching law

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Exceptional (super)algebras (17B25) Analysis on real and complex Lie groups (22E30)

Related Items (9)

On the equivariant 𝐾-theory of the nilpotent cone ⋮ Rings of regular functions on nilpotent orbits 11:model algebras and orbits ⋮ On the multiplicity spaces of spherical subgroups of minimal rank ⋮ Some calculations of the Lusztig-Vogan bijection for classical nilpotent orbits ⋮ Branching rules obtained from explicit correspondences of automorphic representations ⋮ On \(G_2(\mathbb{F}_q)\)-invariants of representations of \(D_4(\mathbb{F}_q)\). ⋮ Unnamed Item ⋮ On quantization of a nilpotent orbit closure in $G_2$ ⋮ The branching problem for generalized Verma modules, with application to the pair (so(7), LieG₂)

Cites Work

• Unipotent representations of complex semisimple groups
• Young-diagrammatic methods for the representation theory of the classical groups of type \(B_ n\), \(C_ n\), \(D_ n\)
• Primitive ideals and nilpotent orbits in type \(G_ 2\)
• The minimal orbit in a simple Lie algebra and its associated maximal ideal
• Generating functions for polynomial irreducible tensors
• Internal Labeling and the Group G2
• Introduction to Lie Algebras and Representation Theory
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