## Lie Groups and Representation Theory

Seminar information archive ～07/20｜Next seminar｜Future seminars 07/21～

Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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### 2012/11/20

16:30-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

On the geometry of discontinuous subgroups acting on some homogeneous spaces (ENGLISH)

**Ali Baklouti**(Sfax University)On the geometry of discontinuous subgroups acting on some homogeneous spaces (ENGLISH)

[ Abstract ]

Let $G$ be a Lie group, $H$ a closed subgroup of $G$ and \\Gamma$ a discontinuous subgroup for the homogeneous space $G/H$. I first introduce the deformation space ${\\mathcal{T}}^{K_o}(\\Gamma, G, H)$ of the action of $\\Gamma$ on $G/H$ in the sense of Kobayashi and some of its refined versions, namely the Clifford--Klein space of deformations of the form ${\\mathcal{X}}=\\Gamma \\backslash G/H$. The deformation space ${\\mathcal{T}}^{G_o}(\\Gamma, G,H)$ of marked $(G,H)$-structures on ${\\mathcal{X}}$ in the sense of Goldman is also introduced. As an important motivation, I will explain the connection between the spaces ${\\mathcal{T}}^{K_o}(\\Gamma, G, H)$ and ${\\mathcal{T}}^{G_o}(\\Gamma, G, H)$ and study some of their topological features, namely the rigidity in the sense of Selberg--Weil--Kobayashi and the stability in the sense of Kobayashi--Nasrin. The latter appears to be of major interest to write down the connection explicitly.

Let $G$ be a Lie group, $H$ a closed subgroup of $G$ and \\Gamma$ a discontinuous subgroup for the homogeneous space $G/H$. I first introduce the deformation space ${\\mathcal{T}}^{K_o}(\\Gamma, G, H)$ of the action of $\\Gamma$ on $G/H$ in the sense of Kobayashi and some of its refined versions, namely the Clifford--Klein space of deformations of the form ${\\mathcal{X}}=\\Gamma \\backslash G/H$. The deformation space ${\\mathcal{T}}^{G_o}(\\Gamma, G,H)$ of marked $(G,H)$-structures on ${\\mathcal{X}}$ in the sense of Goldman is also introduced. As an important motivation, I will explain the connection between the spaces ${\\mathcal{T}}^{K_o}(\\Gamma, G, H)$ and ${\\mathcal{T}}^{G_o}(\\Gamma, G, H)$ and study some of their topological features, namely the rigidity in the sense of Selberg--Weil--Kobayashi and the stability in the sense of Kobayashi--Nasrin. The latter appears to be of major interest to write down the connection explicitly.