Kavli IPMU Komaba Seminar

Seminar information archive ~04/16Next seminarFuture seminars 04/17~

Date, time & place Monday 16:30 - 18:00 002Room #002 (Graduate School of Math. Sci. Bldg.)

2010/11/29

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Scott Carnahan (IPMU)
Borcherds products in monstrous moonshine. (ENGLISH)
[ Abstract ]
During the 1980s, Koike, Norton, and Zagier independently found an
infinite product expansion for the difference of two modular j-functions
on a product of half planes. Borcherds showed that this product identity
is the Weyl denominator formula for an infinite dimensional Lie algebra
that has an action of the monster simple group by automorphisms, and used
this action to prove the monstrous moonshine conjectures.

I will describe a more general construction that yields an infinite
product identity and an infinite dimensional Lie algebra for each element
of the monster group. The above objects then arise as the special cases
assigned to the identity element. Time permitting, I will attempt to
describe a connection to conformal field theory.