# Spinoriality of orthogonal representations of reductive groups

## TL;DR

This paper provides a straightforward criterion to determine when an orthogonal representation of a connected reductive group over a characteristic zero field lifts to the spin group, based on the highest weights of its irreducible components.

## Contribution

It introduces a simple, weight-based criterion for spin-liftability of orthogonal representations of reductive groups, simplifying previous complex methods.

## Key findings

- Criterion based on highest weights for spin-liftability
- Applicable to all orthogonal representations of reductive groups
- Simplifies the analysis of spin structures in representation theory

## Abstract

Let G be a connected reductive group over a field of characteristic zero, and consider an orthogonal representation of G. We give a simple criterion for whether the representation lifts to the spin group, in terms of the highest weights of the irreducible constituents of the representation.