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Equivariant map

About: Equivariant map is a research topic. Over the lifetime, 9205 publications have been published within this topic receiving 137115 citations.


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TL;DR: In this paper, the moment map on the cotangent bundle is used to define a finite cristallographic reflection group Wx, which generalizes the little Weyl group of a symmetric space.
Abstract: Summary. Let G be a connected, reductive group defined over an algebraically closed field of characteristic zero. We assign to any G-variety X a finite cristallographic reflection group Wx by means of the moment map on the cotangent bundle. This generalizes the "little Weyl group" of a symmetric space. The Weyl group Wx is related to the equivariant compactification theory of X. We determine the closure of the image of the moment map and the generic isotropy group of the action of G on the cotangent bundle. As a byproduct we determine the ideal of elements of 11(g) which act trivially on X as a differential operator.

132 citations

Journal ArticleDOI
01 May 1996
TL;DR: In this article, it was shown that G-equivariant topological factors of L/gl × G/P, where the real rank of G is greater than 1, P is a parabolic subgroup of G and G acts diagonally.
Abstract: LetL be a Lie group and λ a lattice inL. SupposeG is a non-compact simple Lie group realized as a Lie subgroup ofL and $$\overline {GA} = L$$ . LetaeG be such that Ada is semisimple and not contained in a compact subgroup of Aut(Lie(G)). Consider the expanding horospherical subgroup ofG associated toa defined as U+ ={geG:a −n gan} →e as n → ∞. Let Ω be a non-empty open subset ofU + andn i → ∞ be any sequence. It is showed that $$\overline { \cup _{i = 1}^\infty a^n \Omega \Lambda } = L$$ . A stronger measure theoretic formulation of this result is also obtained. Among other applications of the above result, we describeG-equivariant topological factors of L/gl × G/P, where the real rank ofG is greater than 1,P is a parabolic subgroup ofG andG acts diagonally. We also describe equivariant topological factors of unipotent flows on finite volume homogeneous spaces of Lie groups.

132 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that if an automorphism of a non-abelian free group $F n$ is irreducible with irreducerible powers, it acts on the boundary of Culler-Vogtmann's outer space with north-south dynamics.
Abstract: We show that if an automorphism of a non-abelian free group $F_n$ is irreducible with irreducible powers, it acts on the boundary of Culler–Vogtmann’s outer space with north–south dynamics: there are two fixed points, one attracting and one repelling, and orbits accumulate only on these points. The main new tool we use is the equivariant assignment of a point $Q(X)$ to any end $X\in\partial F_n$ , given an action of $F_n$ on an $\bm{R}$ -tree $T$ with trivial arc stabilizers; this point $Q(X)$ may be in $T$ , or in its metric completion, or in its boundary. AMS 2000 Mathematics subject classification: Primary 20F65; 20E05; 20E08

132 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that if a discrete structure is associated to a sprinkling in an intrinsic manner, then the structure will not pick out a preferred frame, locally or globally.
Abstract: This paper concerns random sprinklings of points into Minkowski spacetime (Poisson processes). It proves that there exists no equivariant measurable map from sprinklings to spacetime directions (even locally). Therefore, if a discrete structure is associated to a sprinkling in an intrinsic manner, then the structure will not pick out a preferred frame, locally or globally. This implies that the discreteness of a sprinkled causal set will not give rise to "Lorentz breaking" effects like modified dispersion relations. Another consequence is that there is no way to associate a finite-valency graph to a sprinkling consistently with Lorentz invariance.

131 citations

Journal ArticleDOI
TL;DR: In this paper, the homotopy theory of motivic spaces and spectra parametrized by quotient stacks [X / G ], where G is a linearly reductive linear algebraic group, is studied.

131 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
2023463
2022888
2021630
2020658
2019526