248-dimension maths puzzle solved

Paul_G

Regular
I've dropped on this board a few times and noticed some of you quite enjoy stuff of an advanced mathematical nature. Me? I think it's cool, but i don't really understand a lot of the higher level stuff (Anything with more symbols than numbers is way too much for me). Anyway i figured this might appeal to some of you. Simple old me was far more impressed by this particular statistic

BBC News Story said:
The team calculated that if all the numbers were written out in small type, they would cover an area the size of Manhattan.

So if anyone here understands this stuff please, if possible, i'd love to understand.
 
The BBC story claims it's the most complicated, but doesn't the monster group have more symmetry, a higher order, and more dimensions?
 
I believe thats an error. However its likely a simple blunder by the journalist since the monster group is not a lie group, but rather a sporadic group. But yes indeed the monster group is far and away the largest simple group.

I must admit the Kazhdan–Lusztig polynomial calculation is opaque to me. They are related to things I do understand, like flag varieties and R polynomials, but the computations thereof are a complete mystery to me. I do not know if similar calculations where done for the monster group, though I very much doubt it as they would intuitively be prohibitively expensive.
 
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