MS Seminar (Mathematics - String Theory)

Speaker: Gurbir Dhillon (Yale University)
Title: Phantom minimal series and a Peter--Weyl theorem for loop groups
Date (JST): Thu, Nov 17, 2022, 13:30 - 15:00
Place: Hybrid
Abstract: Let G be a complex reductive group. The celebrated Peter--Weyl theorem decomposes the algebra of functions on G as a G x G module with respect to left and right translations. In this talk we introduce a natural analogue for the loop group G((z)). A key role is played by a family of G((z)) representations at negative level, the phantom minimal series. These are dual, in a precise but somewhat subtle homological sense, to the more familiar positive energy representations at positive level. Time permitting, we will discuss the existence of phantom minimal series for many related vertex algebras, and some interesting analytic properties of their characters.