Tagged Questions
1
vote
0answers
30 views
Usage and determination of “rank” and “dimension” of groups & representations
Physicist here. I seem to see conflicting statements about the rank of some groups I've come across lately.
A paper I'm reading states that $SO(6)$ is rank 3 and therefore its Cartan subalgebra ...
0
votes
1answer
37 views
preserves eigen spaces?
"Let $H_0=\begin{pmatrix}i&0\\0&-i\end{pmatrix}$, suppose $A\in SU(2)$ commutes with $H_0$, it must preserves each eigen spaces for $H_0$, eigen spaces for $H_0$ are just $\mathbb{C}e_1$ and ...
0
votes
2answers
31 views
Understanding the Lie algebra $o_{V,B}$
I am learning about Lie algebras and I do not understand the following subalgebra of $\mathfrak gl_{V}$. Let $V$ be a vector space and $\mathfrak gl_{V}$ be the Lie algebra of endomorphisms on $V$. ...
6
votes
0answers
88 views
Why are parabolic subgroups called “parabolic” subgroups?
I used to think that things called "parabolic" must have something to do with parabolas or their defining quadratic equations. In fact, terms like parabolic coordinate, parabolic partial differential ...
1
vote
1answer
168 views
What is meant by “direct summand in a tensor product”?
I am currently working on the topic of Lie - Algebras and I have stumbled a few times over the expression "direct summand in a tensor product".
The text says that $\ V(\lambda) $ as an ...
