# 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.

## Key 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.