Let Γ be a finite group acting on a simple Lie algebra 𝔤 and acting on an s-pointed projective curve (Σ, p = {p1, . . . ,ps}) faithfully (for s ≥ 1). Also, let an integrable highest weight module Hc(λi) of an appropriate twisted affine Lie algebra determined by the ramification at pi with a fixed central charge c is attached to each pi. We prove that the space of twisted conformal blocks attached to this data is isomorphic to the space associated to a quotient group of Γ acting on 𝔤 by diagram automorphisms and acting on a quotient of Σ. Under some mild conditions on ramification types, we prove that calculating the dimension of twisted conformal blocks can be reduced to the situation when Γ acts on 𝔤 by diagram automorphisms and covers of ℙ1 with 3 marked points. Assuming a twisted analogue of Teleman’s vanishing theorem of Lie algebra homology, we derive an analogue of the Kac-Walton formula and the Verlinde formula for general Γ-curves (with mild restrictions on ramification types). In particular, if the Lie algebra 𝔤 is not of type D4, there are no restrictions on ramification types.
This is joint work with Jiuzu Hong.
This video is part of the conference Representation Theory and Geometry that took place at the University of Georgia.
