rafaelm

Zagreb, Croatia

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28
comment Root spaces for symplectic Lie algebra $\mathfrak{s} \mathfrak{p}_n$
The letter one. You can check by definition of root subspace. The first one $E_{1,2}+E_{n+2,n+1}$ is not in $\mathfrak{sp}$.
Nov
28
revised Root spaces for symplectic Lie algebra $\mathfrak{s} \mathfrak{p}_n$
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Nov
28
comment Root spaces for symplectic Lie algebra $\mathfrak{s} \mathfrak{p}_n$
If you take a matrix from $\mathfrak{sp}$, then its lower right block is the negative transpose of the left upper block. That does not apply to root subspaces (big matrix in my answer), because taking negatives does not land you in the opposite root subspace, but stays in the same subspace. I will edit it in my answer to make it more clear.
Nov
28
comment Root spaces for symplectic Lie algebra $\mathfrak{s} \mathfrak{p}_n$
So $\mathfrak{g}_{b_i}$ is one dimensional span of the matrix $E_{i,n+i}$ (which has $1$ on the coordinates $(i,n+i)$, and $0$'s elswhere). That is why $b_i$ is written on the position $(i,n+i)$ in the above answer. In the same way $\mathfrak{g}_{-b_i}$ is span of $E_{n+i,i}$.
Nov
28
answered Root spaces for symplectic Lie algebra $\mathfrak{s} \mathfrak{p}_n$
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11
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12
accepted Horizontal alignment of tikzpicure in an equation
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12
comment Horizontal alignment of tikzpicure in an equation
The problem is that in the theory I am writing about, \node[above] has different meaning than \node[below].
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12
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revised Sections of inverse image sheaf of sheaf of sections of vector bundle
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revised Sections of inverse image sheaf of sheaf of sections of vector bundle
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