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arXiv · 1808.02363

Geometric Matrices and the Symmetric Group

Garret Sobczyk
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Abstract

We construct real and complex matrices in terms of Kronecker products of a Witt basis of 2n null vectors in the geometric algebra over the real and complex numbers. In this basis, every matrix is represented by a unique sum of products of null vectors. The complex matrices provide a direct matrix representation for geometric algebras with signatures p+q <= 2n+1. Properties of irreducible representations of the symmetric group are presented in this geometric setting.

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Garret Sobczyk. 2018-08-02. Geometric Matrices and the Symmetric Group. https://doi.org/10.13140/rg.2.2.24843.80160

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