Conformal blocks attached to twisted groups

TL;DR

This paper extends the concept of conformal blocks to cases involving Galois coverings of curves, resulting in a sheaf on the Hurwitz stack that retains key properties like fusion rules and the WZW connection.

Contribution

It introduces a generalized framework for conformal blocks associated with twisted groups over covering data of curves, broadening their applicability.

Findings

Sheaves of conformal blocks are constructed on the Hurwitz stack.

Classical properties such as fusion rules are preserved in the new setting.

The WZW connection and propagation of vacua are established for the generalized sheaves.

Abstract

The aim of this paper is to generalize the notion of conformal blocks to the situation in which the Lie algebra they are attached to is not defined over a field, but depends on covering data of curves. The result will be a sheaf of conformal blocks on the Hurwitz stack parametrizing Galois coverings of curves. Many features of the classical sheaves of conformal blocks are proved to hold in this more general setting, in particular the fusion rules, the propagation of vacua and the WZW connection.