rafaelm

Zagreb, Croatia

 Nov 28 awarded Yearling Nov 28 awarded Yearling Nov 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\$added 36 characters in body 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\$ Nov 11 awarded Critic Aug 21 awarded Popular Question Jul 12 accepted Horizontal alignment of tikzpicure in an equation Jul 12 comment Horizontal alignment of tikzpicure in an equationThe problem is that in the theory I am writing about, \node[above] has different meaning than \node[below]. Jul 12 asked Horizontal alignment of tikzpicure in an equation Jun 15 awarded Civic Duty Apr 19 awarded Nice Answer Mar 6 awarded Tumbleweed Mar 4 revised Sections of inverse image sheaf of sheaf of sections of vector bundleadded 8 characters in body Mar 4 asked Sections of inverse image sheaf of sheaf of sections of vector bundle Feb 28 revised Sections of inverse image sheaf of sheaf of sections of vector bundleedited body Feb 27 asked Sections of inverse image sheaf of sheaf of sections of vector bundle Dec 8 awarded Caucus