Okay, everyone else has mentioned this, so I suppose I should too: A team considering the one-dimensional Ising model of ferromagnetism has found some evidence they claim is linked to certain symmetry; an action of the Lie group $E_8$ on the space of states which preserves some interesting property or another. I can’t read the full paper myself, but John Baez discusses it a bit at the beginning of the most recent This Week’s Finds.

Now those of you who have been reading for a while might be thinking, “Eee-eight.. doesn’t that sound familiar from somewhere?” Well, actually those of you who have been reading for a while are probably experienced mathematicians and know all about $E_8$ to begin with but work with me here, people.

Ahem.

So, yes, we have talked about $E_8$ here! Back in the spring of 2007 as this whole project was just getting off the ground, the Atlas of Lie Groups project announced that they’d completed calculating the Kazhdan-Lusztig-Vogan polynomial for the split real form of $E_8$. Immediately, I gave a quick overview of the idea of a Lie group, a Lie algebra, and a representation; a rough overview for complete neophytes of what, exactly, had been calculated; and an attempt to explain why we should care. All with the promise of more information eventually.

Of course it was the fall of 2008 before I even defined a group representation in the main exposition, so some of this information has been a long time coming. But still, what progress we’ve made! Of course, we’re not up to the point of really understanding Zuckerman’s three lectures, but all in good time.

I have, though, been inspired to think about a nice little toy geometry problem to talk about as my coverage of Riemann integration winds down.