Hauptseminar Symplektische Geometrie

In order to generalize Thurston's laminations to a split real G-higher Teichmüller space, one is naturally led to make use of the (spherical) affine Hecke algebra of G. If as a toy model one instead considers the Hecke algebra of a finite Coxeter system or more generally a symmetric algebra of finite rank, the same construction yields an open-closed 2d topological quantum field theory (TQFT). It associates an element of the base ring to any punctured surface - for example, a Laurent polynomial with integer coefficients when the symmetric algebra is a Hecke algebra. These Laurent polynomials have only positive coefficients when the Coxeter system is of classical type or exceptional type H3, E6 and E7, a fact that we now understand from the representation theory of the corresponding Hecke algebra.

Mittwoch, den 19. Januar 2022 um 11:15 Uhr, in Zoom, Online Mittwoch, den 19. Januar 2022 at 11:15, in Zoom, Online