The Structure of Parabolic Subgroups

By Kenneth D. Johnson. Journal of Lie theory, 2004

90 citations recorded by the source corpus.

Suppose G is a real connected simple noncompact Lie group with (using standard notation) Iwasawa decomposition G = KAN . If M = Z(A)\K, the group B = MAN is a minimal parabolic subgroup of G. Since A is a vector group and N is a simply connected nilpotent group, the topological structure of B is determined by the structure of M. When G is a linear group the structure of M is well known. However, if G is not a linear group there is very little available information about M. Our purpose here is to give a description of the group M for any connected, simply connected, nonlinear simple group G.

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/936f8357aa9045c84256e8720d1493380ab01e9f

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Citations in the corpus

Elementary subgroups of isotropic reductive groups (2009, unknown): “[4]) if there exists a root α ∈ Φ \ ∆ with αJ = a.”
Generation of finite almost simple groups by conjugates (2003, methodology): “By [4], U/Φ(U) is an irreducible and restricted FqJ ′-module.”
Fuchsian groups, finite simple groups and representation varieties (2005, background): “By [2], there is an L-invariant central series 1 = Q0 / Q1 / ∙ ∙ ∙ / Ql = Q such that each factor Qi/Qi−1 has the structure of an irreducible L-module over Fq (or possibly an extension field if G is twisted).”
The maximal subgroups of positive dimension in exceptional algebraic groups (2004, background): “It follows from [3] that W3 affords the irreducible representation, VD5(λ5) (a maximal vector is given by e23465321).”