27 Feb
2010
27 Feb
'10
3:15 p.m.
A typographical eagle points out that the earlier
where K = [[1,0],[0,-1]] is the canonical skew-symmetric matrix
should obviously have read
where K = [[0,-1],[1,0]] is the canonical skew-symmetric matrix
Sp(4) of course needs instead K = [[0,0,0,-1],[0,0,-1,0],[0,1,0,0],[1,0,0,0]]; or perhaps K = [[0,-1,0,0],[1,0,0,0],[0,0,0,-1],[0,0,1,0]]. And while I'm at it, I have just realised that
[the] central problem is whether these matrices comprise a vector space
is a gross over-simplification. Rather, it's whether, somewhere within the dimension-11 GSp(4), there exists a dimension-4 vector space, which then generates the whole group via multiplication. (Sigh ...) WFL