arXiv math/03041852003-04-14math.RT

A convexity property for real orbits in complexified Riemannian symmetric spaces

Bernhard Kroetz

备注：: 13 pages
发表信息：: Math. Res. Letters 11 no. 2-3 (2004), 197-211

英文摘要：

A convexity theorem for certain G-orbits in a complexified Riemannian symmetric space G_C/K_C is proved. Applications to analytically continued spherical functions will be given.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Representation theory, Radon transform and the heat equation on a Riemannian symmetric space

Let X=G/K be a Riemannian symmetric space of the noncompact type. We give a short exposition of the representation theory related to X, and discuss its holomorphic extension to the complex crown, a G-invariant subdomain in the complexified symmetric space X_\C=G_\C/K_\C. Applications to the heat transform and the Radon transform for X are given.

2007-07-05math.RT

Invariant Stein domains in Stein symmetric spaces and a non-linear complex convexity theorem

We prove a complex version of Kostant's non-linear convexity theorem. Applications to the construction of G-invariant Grauert tubes of non-compact Riemannian symmetric G/K spaces are given.

2001-10-17math.CVmath.RT

Moment maps and Riemannian symmetric pairs

The main result of this paper is a ``real form'' of Kirwan's convexity theorem, which in the abelian case was proved earlier by Duistermaat. We apply our result to flag varieties of real semisimple groups and obtain eigenvalue inequalities, which generalize inequalities found by Weyl, Ky Fan, Kostant, Klyachko, and many others.

1999-11-25math.AGmath.RTmath.SG

Complex extensions of semisimple symmetric spaces

Let G/H be a pseudo-Riemannian semisimple symmetric space. The tangent bundle T(G/H) contains a maximal G-invariant neighbourhood of the zero section where the adapted complex structure exists. Such neighbourhood is endowed with a canonical G-invariant pseudo-Kaehler metric of the same signature as the metric on G/H. We use the polar map from T(G/H) to the complexified symmetric space G^C/H^C to define a G-invariant pseudo-Kaehler metric on distinguished G-invariant domains in G^C/H^C or on coverings of principal orbit strata in G^C/H^C.

2006-03-03math.CVmath.RT

The Riemannian geometry of orbit spaces. The metric, geodesics, and integrable systems

We investigate the rudiments of Riemannian geometry on orbit spaces $M/G$ for isometric proper actions of Lie groups on Riemannian manifolds. Minimal geodesic arcs are length minimising curves in the metric space $M/G$ and they can hit strata which are more singular only at the end points. This is phrased as convexity result. The geodesic spray, viewed as a (strata-preserving) vector field on $TM/G$, leads to the notion of geodesics in $M/G$ which are projections under $M\to M/G$ of geodesics which are normal to the orbits. It also leads to `ballistic curves' which are projections of the other…

2001-02-20math.DGmath.RTmath.SG