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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

-1 votes

Automorphism group of real orthogonal Lie groups

Check the book Freudenthal Linear Lie groups, in this book you find a complete treatment of Aut(G) for G a real semisimple (connected) Lie group. best regards
jorge vargas's user avatar
0 votes

Automorphism group of real orthogonal Lie groups

also check Onishchik: Lectures on Real Semisimple Lie Algebras and Their Representations.
jorge vargas's user avatar
1 vote

Automorphism group of real orthogonal Lie groups

on page 386 (paragraph 66.7) you find the table Out(G)/Int(G) on page 387 you find D_{l,j} j>1 your Lie algebras so(p,q) when your p or q is even. on page 391 you find so(p,q) when both p,q are odd T …
jorge vargas's user avatar
2 votes

How can one show $G/T$ is a coadjoint orbit for a compact Lie group $G$ and $T$ its maximal ...

Fix a regular element $\lambda$ in $Lie(T)\subset Lie(G)$, then the coadjoint orbit $Ad(G) \lambda$ is isomorphic to $G/T.$ Best,
jorge vargas's user avatar
-1 votes

Is $M=E_{7(7)}/SU(7)\times\mathbb{R}^{+}$ a (pseudo)Kähler-Hodge manifold? Open problem

If i am not wrong the following is true, G compact connected Lie group, H the centralizer of a torus in G, then G/H is a projective manifold, does this answer your question??
jorge vargas's user avatar
2 votes

Branching laws for $SO(n)$

It is not multiplicity free..., check the green book of Antony Knapp, or else the old book of Zelobenko, compact.....
jorge vargas's user avatar
2 votes

Branching laws for $SO(n)$

check Eastwood-Wolf, branchig of ...., Arxive 0812.0822 math[RT] in this paper you find who to compute branching laws useing LiE.
jorge vargas's user avatar