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Results tagged with symmetric-spaces
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user 89948
A symmetric space is a connected Riemannian manifold in which at every point there exists a global self-isometry whose differential at the given point is minus identity.
7
votes
Spherical roots, restricted roots, and the dual group of a symmetric variety
There is a small survey published in an Oberwolfach report by Bart Van Steirteghem comparing the different normalizations of spherical roots in more detail. The standard normalization is obtained by d …
- 15.5k
5
votes
Accepted
Irreducible Symmetric Pairs
It is true that $\mathfrak p$ is always an irreducible $\mathfrak k$-module. Be aware though that the complexification $\mathfrak p_{\mathbb C}$ might be reducible as an $\mathfrak k_{\mathbb C}$-modu …
- 15.5k
4
votes
Non-semisimple symmetric subgroups of simply connected simple algebraic groups
In your case, $H$ is a Levi subgroup and the derived subgroup of a Levi subgroup in a simply connected group is always simply connected (since all fundamental weights are characters).
- 15.5k
12
votes
Accepted
Is SO(2n+1)/U(n) a symmetric space?
Let me complement Claudio's answer. There is indeed a definition of symmetric space which works for any Riemannian manifold $M$: For any point $p\in M$ there is an involutive isometry $\iota_p$ of $M$ …
- 15.5k