Conformal blocks in the tensor product of vector representations and localization formulas

TL;DR

This paper presents a new polynomial formula for conformal blocks at level one on the sphere using equivariant localization, and extends this to generate conformal blocks at any level for generic points.

Contribution

It introduces a polynomial formula for level one conformal blocks and provides a generating set for conformal blocks at any level with generic marked points.

Findings

Polynomial formula for conformal blocks at level one

Generating set for conformal blocks at arbitrary levels

Applicable to generic marked points on the sphere

Abstract

Using equivariant localization formulas we give a formula for conformal blocks at level one on the sphere as suitable polynomials. Using this presentation we give a generating set in the space of conformal blocks at any level if the marked points on the sphere are generic.