# Spinor Representation of Conformal Group and Gravitational Model

## TL;DR

This paper explores spinor representations of the conformal group and develops a gravitational model invariant under local transformations using a 15-dimensional vector spacetime derived from the adjoint representation of SO(2,4).

## Contribution

It introduces a novel gravitational model based on spinor representations of the conformal group within a 15-dimensional spacetime framework.

## Key findings

- Constructed a spacetime from 15-dimensional vectors in the adjoint of SO(2,4)
- Developed a conformally invariant gravitational model
- Demonstrated local invariance of the gravitational theory

## Abstract

We consider spinor representations of the conformal group. The spacetime is constructed by the 15-dimensional vectors in the adjoint representation of $SO(2,4)$. On the spacetime, we construct a gravitational model that is invariant under local transformation.