Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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|improve this question
add comment

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.