共查询到20条相似文献,搜索用时 0 毫秒
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Michael Field 《Proceedings of the American Mathematical Society》1999,127(11):3361-3365
Let be a compact connected semisimple Lie group. We prove that the subset of consisting of pairs which topologically generate is Zariski open.
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András Domokos Roland EsquerraBob Jaffa Tom Schulte 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(14):4642-4652
In this paper, we consider a natural subelliptic structure in semisimple, compact and connected Lie groups, and estimate the constant in the so-called subelliptic Friedrichs-Knapp-Stein inequality, which has implications in the regularity theory of p-energy minimizers. 相似文献
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Mohammad Shafiee 《Journal of Geometry》2014,105(3):615-623
In this paper a compact and semisimple Lie group G is considered endowed with a 2-plectic structure ω, induced by the Killing form. We show that the Lie group of 2-plectomorphisms of G is finite dimensional and compact, and hence the Darboux’s theorem fails to be true for this 2-plectic structure. Also it is shown that ω induces a left-invariant \({\mathfrak{g}^{*}}\) valued 2-form which is proportional to dΘ, where Θ is the Cartan–Maurer 1-form on G. At last we consider the action of G on its tangent bundle which is furnished with the 2-plectic structure ω c , the complete lift of ω, and calculate covariant momentum map of this action. 相似文献
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In this article, we introduce a new method for manufacturing harmonic morphisms from semi-Riemannian manifolds. This is employed
to yield a variety of new examples from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with their standard Riemannian metrics. We develop a duality principle and show how this can be used to construct
the first known examples of harmonic morphisms from the non-compact Lie groups , SU
*(2n), , SO
*(2n), SO(p, q), SU(p, q) and Sp(p, q) equipped with their standard dual semi-Riemannian metrics.
相似文献
6.
Christopher Meaney 《Journal of Functional Analysis》1982,48(1):43-57
Let G be a compact connected semisimple Lie group with Lie algebra . We show that the conjugacy class of a regular element of G is not a set of synthesis for the Fourier algebra of G. Similarly, the Ad(G)-orbit of a regular element of is not a set of synthesis for the algebra of Fourier transforms on . In proving this latter result we demonstrate a regularity property of Ad-invariant Fourier transforms, analogous to the differentiability of radial Fourier transforms. 相似文献
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José Garcí a-Cuerva José Manuel Marco Javier Parcet 《Transactions of the American Mathematical Society》2003,355(9):3591-3609
Sharp Fourier type and cotype of Lebesgue spaces and Schatten classes with respect to an arbitrary compact semisimple Lie group are investigated. In the process, a local variant of the Hausdorff-Young inequality on such groups is given.
9.
Sigmundur Gudmundsson Martin Svensson 《Differential Geometry and its Applications》2006,24(4):351-366
In this paper we prove the local existence of complex-valued harmonic morphisms from any compact semisimple Lie group and their non-compact duals. These include all Riemannian symmetric spaces of types II and IV. We produce a variety of concrete harmonic morphisms from the classical compact simple Lie groups SO(n), SU(n), Sp(n) and globally defined solutions on their non-compact duals SO(n,C)/SO(n), SLn(C)/SU(n) and Sp(n,C)/Sp(n). 相似文献
10.
Harish-Chandra 《Acta Mathematica》1965,113(1):241-318
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In this paper we classify the subsemigroups of any connected semisimple Lie groupG which areK-bi-invariant, whereG=KAN is an Iwasawa decomposition ofG. 相似文献
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《Comptes Rendus Mathematique》2019,357(9):697-707
For a semisimple Lie group G satisfying the equal rank condition, the most basic family of unitary irreducible representations is the discrete series found by Harish-Chandra. In this paper, we study some of the branching laws for these when restricted to a subgroup H of the same type by combining the classical results with the recent work of T. Kobayashi. We analyze aspects of having differential operators being symmetry-breaking operators; in particular, we prove in the so-called admissible case that every symmetry breaking (H-map) operator is a differential operator. We prove discrete decomposability under Harish-Chandra's condition of cusp form on the reproducing kernels. Our techniques are based on realizing discrete series representations as kernels of elliptic invariant differential operators. 相似文献
15.
Let G be a compact Lie group and A a G-space. When does there exist a relative G-CW-complex (X,A) with free G-action on X\A, such that X has the homology of a sphere? This paper gives sufficient conditions, which can be used for the construction of homotopy representations. 相似文献
16.
Holomorphic diffeomorphisms of complex semisimple Lie groups 总被引:2,自引:0,他引:2
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We prove new estimates for spherical functions and their derivatives on complex semisimple Lie groups, establishing uniform
polynomial decay in the spectral parameter. This improves the customary estimate arising from Harish-Chandra's series expansion,
which gives only a polynomial growth estimate in the spectral parameter. In particular, for arbitrary positive-definite spherical
functions on higher rank complex simple groups, we establish estimates for which are of the form in the spectral parameter and have uniform exponential decay in regular directions in the group variable a
t
. Here is an explicit constant depending on G, and may be singular, for instance.?The uniformity of the estimates is the crucial ingredient needed in order to apply classical
spectral methods and Littlewood—Paley—Stein square functions to the analysis of singular integrals in this context. To illustrate
their utility, we prove maximal inequalities in L
p
for singular sphere averages on complex semisimple Lie groups for all p in . We use these to establish singular differentiation theorems and pointwise ergodic theorems in L
p
for the corresponding singular spherical averages on locally symmetric spaces, as well as for more general measure preserving
actions.
Submitted: May 2000, Revised version: October 2000. 相似文献