Results 231 to 240 of about 100,933 (264)

Branching Rules for Simple Lie Groups

Journal of Mathematical Physics, 1965
If Γ is an irreducible representation of a group 𝒢, and ℋ is a subgroup of 𝒢, then Γ furnishes a representation of ℋ which is, in general, reducible, and the branching rules specify which irreducible representations of ℋ occur in the decomposition of this representation.
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Construction of invariants for simple lie groups

Nuclear Physics, 1964
Abstract A coupling coefficient for the orthogonal and symplectic groups is defined.It can be utilized to construct a set of invariants and it is proved that these are all the independent invariants of the considered groups excepting the orthogonal group in even dimensions for which an invariant cannot be constructed in a similar way.
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The Betti Numbers of the Simple Lie Groups

Canadian Journal of Mathematics, 1958
The purpose of the present paper1 is to simplify the calculation of the Betti numbers of the simple compact Lie groups.For the unimodular group and the orthogonal group on a space of odd dimension the form of the Poincaré polynomial was correctly guessed by E. Cartan in 1929 (5, p. 183). The proof of his conjecture and its extension to the four classes
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Semigroups of Simple Lie Groups and Controllability

Journal of Dynamical and Control Systems, 2013
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The Dual Space of Semi-Simple Lie Groups

American Journal of Mathematics, 1969
Introduction. This paper is inspired by Kazhdan's work [8]. In [8], he has studied the structure of lattices, i.e., discrete subgroups with finite invariant measure on the factor space, of a Lie group by investigating a particular topological property of the dual space of a Lie group. Let G be a separable locally compact group and G its dual space.
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Dynamics of Simple Lie Groups on Lorentz Manifolds

Geometriae Dedicata, 2004
In [``Noncompact simple automorphism groups of Lorentz manifolds and other geometric manifolds'', Ann. Math. (2) 144, No. 3, 611--640 (1996; Zbl 0871.53048)], \textit{N. Kowalsky} proved that a connected simple Lie group with finite center acting nontriavially, nonproperly and isometrically on a connected Lorentz manifold is locally isomorphic to ...
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Finite simple unisingular groups of Lie type

Journal of Group Theory, 2003
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Guralnick, Robert M., Pham Huu Tiep
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Cartan Decompositions and Semigroups of Simple Lie Groups

Journal of Lie Theory, 2018
Let G be a split real connected simple Lie group and S a semigroup of G that contains a subgroup G(α) for an arbitrary root α, isomorphic to SL(2,R). We present a Cartan decomposition of the Lie algebra of G, related to α, invariant by the adjoint action of the Lie algebra sl(2,R) that allows to characterize some properties of the Lie saturate of the ...
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A Poisson Formula for Semi-Simple Lie Groups

The Annals of Mathematics, 1963
for some bounded function h on the boundary of the disc. The function h(z) determines a function h(g) on G by setting h(g) = h(g(O)). If h(z) is harmonic, it may be shown that h(g) is annihilated by a certain class of differential operators on G. The Poisson formula (1) may be used to express h(g), and we find that here it takes on a particularly ...
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Commutators in Finite Simple Groups of Lie Type

Bulletin of the London Mathematical Society, 2000
Summary: Using properties of the Steinberg character, we obtain a congruence modulo \(p\) for the number of ways in which a \(p\)-regular element may be expressed as a commutator in a finite simple group \(G\) of Lie type of characteristic \(p\). This congruence shows that such an element is a commutator in \(G\).
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