A classification of four-tuples of spinors of a ten dimensional space

TL;DR

This paper classifies the orbits of a specific group action on a tensor product of spinor and natural modules in ten-dimensional space using Vinberg's theta-groups and computational algebra.

Contribution

It introduces a novel classification of four-tuples of spinors in ten dimensions by combining theoretical and computational methods.

Findings

Complete orbit classification achieved

Application of Vinberg's theta-groups to spinor modules

Use of GAP4 for complex algebraic computations

Abstract

We use the theory of theta-groups developed by Vinberg, along with computations in the computer algebra system GAP4, to classify the orbits of Spin(10,C)x SL(4,C) acting on the tensor product of the half spin module of Spin(10,C) and the natural module of SL(4,C).