This is about Deligne's "La série exceptionnelle de groupes de Lie, C.R. Acad. Sci. Paris Sér. I Math. 322 (1996), no. 4, 321–326". 


When this came out, that was quite something! People were often talking about it, at lunch or coffee time - even making bets if I remember well.


I totally lost contact with all this, since then, now I see that there is a lot of literature on all this, for the most very technical, and I was curious: is there any survey paper or blog post or anything, which explains (for non-specialists) the status of that conjecture of Deligne? I mean, if that mysterious category exists, and what is it.


Many thanks.



Deligne's 1996 note on exceptional Lie groups
My understanding is that the series corresponding to the first three rows of the magic square do not exist but the existence of the series for the last row, the original exceptional series, is still open. This follows from Dylan Thurston's (unpublished) computer calculation and from Pierre Vogel's (unpublished) papers.


