All Questions
Tagged with symmetric-spaces exceptional-groups
7 questions
6
votes
2
answers
512
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Constructing real forms of the Tits-Freudenthal magic square for (Rosenfeld) projective planes
If $\mathbb{K},\mathbb{L} \in \{\mathbb{R},\mathbb{C},\mathbb{H},\mathbb{O}\}$ then the Rosenfeld projective ("elliptic"?) plane $\mathbb{P}^2(\mathbb{K}\otimes\mathbb{L})$ is "the" compact Riemannian ...
- 32.4k
4
votes
0
answers
145
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Exceptional symmetric spaces with quaternionic structure
Following this and this question I found following chain of exceptional symmetric spaces being quaternionic manifolds. I listed dimensions as superscripts for reader convenience.
$F_{I}^{28}\subset ...
user21230
4
votes
0
answers
187
views
A few questions about $E_7$ and its symmetric spaces
My question about $E_6$ survived, so I post next episode. From the Yokota book I found out that there is $-1$ in $E_7$ Lie group. This book defines Lie group $E_7$ using 56-dimensional Freudenthal ...
user21230
7
votes
0
answers
601
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A few questions about $E_6$ and its symmetric spaces
Preface
The purpose of my question - on high level - is to understand exceptional symmetric spaces. My latest idea is to embed them into Lie group. There is quite nice embedding of 32-dimensional $E_{...
user21230
6
votes
0
answers
272
views
Exceptional symmetric spaces embedded in exceptional Lie group
In Yokota (1959) and Atsuyama (1977) papers one can find embedding of projective space $\mathbb OP^2$ into Lie group $F_4$. Lately I come to following idea to have embedding of all four projective ...
user21230
22
votes
2
answers
1k
views
Does $\mathrm{E}_7/(\mathrm{SU}_8/(\mathbb{Z}/2))$ carry an almost complex structure?
Recall the list of irreducible simply connected inner symmetric spaces of compact type in dimension $4k+2$:
Hermitian symmetric spaces (one can write them down explicitly);
Grassmannians of oriented ...
- 2,140
21
votes
2
answers
1k
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Geometric interpretation of exceptional symmetric spaces
Elie Cartan has classified all compact symmetric spaces admitting a compact simple Lie group as their group of motion.There are 7 infinite series and 12 exceptional cases. The exceptional cases are ...
- 3,022