# Tag Info

## Hot answers tagged lie-groups

13 votes
Accepted

### Maximum symmetry metric on $\mathbb{C}P^n$

There's an easy counterexample to your guess: Let $M^6 = \mathrm{SU}(3)/\mathbb{T}^2$, where $\mathbb{T}^2\subset\mathrm{SU}(3)$ is the maximal torus (for example, the diagonal subgroup). In that ...
• 101k
5 votes

### Description of the generalized grassmannians and flag varieties (parabolic quotients) associated to the exceptional groups

Definitely not a full answer (and rather late to the party) but I am interested in the $E_7$ case myself so I have been doing a little computing of the dimensions of these flags that I thought was ...
• 747
5 votes
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### Injectivity of the cohomology map induced by some projection map

Ok, I will follow Fernando's advice and post an answer. I learned the computation below from the beginning of Pin(2)-equivariant Seiberg--Witten Floer homology and the triangulation conjecture. The ...
• 8,728
5 votes
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### Question about maximal compact subgroups of Lie groups

• 9,057
5 votes

• 8,728
2 votes
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• 50.1k
1 vote

### Counting adjoints in the symmetric or antisymmetric square of a Lie group representation

I don't have a proof but I noticed some things while having a quick look for some counterexamples that I thought were worth sharing. First things first what you are looking for is not special to the ...
• 747

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