Lie Groups and Representation Theory

Seminar information archive ~03/27Next seminarFuture seminars 03/28~

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

2007/05/25

16:00-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)
金行壮二 (上智大学名誉教授)
Causalities, G-structures and symmetric spaces
[ Abstract ]
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 $M$.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070525kaneyuki