MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

On MO I learnt about the two-variable E7 polynomial (status: conjectural). What about a two-variable E8 polynomial? I have reasons to believe such a thing exists too, but I do magic, not math, so my opinions are irrelevant. :-) The only thing my research gave on the E8 family (and the two-variable E8 polynomial should generalize it like the E7 one the E7 family) was "Birdtracks". So, please check a)Never heard of! b)Circumstantial Evidence c)Proven, see...

Side notes (may be ignored): Magic has certain advantages, so just in case the result is unknown yet (and knowing the result beforehand always helps), here are my skein relations for the S matrix of those polynomials:
(S+Y^2/Z^6*I)(S-Y*I)(S-Z*I)(S+1/Z^3*I)=0 (E7)
(S-Z^6*I)(S-Z^3*I)(S+I)(S-Y*I)(S+Z/Y*I)=0 (E8)
Y and Z are the two variables, I the identity matrix, and "polynomial" it isn't. (At least not in Y and Z. For Y=+-Z^p and the right p, you'll get back the polynomials of the members of the E7/E8 families. I would give a result for E6 too...if not duality would interfere with my magic :-)

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.