## Lie群論・表現論セミナー

開催情報 火曜日　16:30～18:00　数理科学研究科棟(駒場) 126号室 小林俊行 https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007年05月25日(金)

16:00-17:30   数理科学研究科棟(駒場) 122号室
いつもと曜日時刻がちがいますのでご注意ください

Causalities, G-structures and symmetric spaces
[ 講演概要 ]
Let M be an $n$-dimensional smooth manifold, $F(M)$ the frame bundle of $M$, and let $G$ be a Lie subgroup of $GL(n,\\mathbb R)$. We say that $M$ has a $G$-structure, if there exists a principal subbundle $Q$ of $F(M)$ with structure group $G$. Let $C$ be a causal cone in $\\mathbb R^n$, and let $Aut C$ denote the automorphism group of $C$.

Starting from a causal structure $\\mathcal{C}$ on $M$ with model cone $C$, we construct an $Aut C$-structure $Q(\\mathcal{C})$. Several concepts on causal structures can be interpreted as those on $Aut C$-structures. As an example, the causal automorphism group $Aut(M,\\mathcal{C})$ of $M$ coincides with the automorphism group $Aut(M,Q(\\mathcal{C}))$ of the $Aut C$-structure.

As an application, we will consider the unique extension of a local causal transformation on a Cayley type symmetric space $M$ to the global causal automorphism of the compactification of $M$.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070525kaneyuki