Representation of the Symmetric Group

Garret Sobczyk
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Garret Sobczyk: Universidad de Las Américas, Departamento de Física y Matemáticas

Chapter Chapter 12 in New Foundations in Mathematics, 2013, pp 201-222 from Springer

Abstract: Abstract Over the last 112 years since Frobenius and Burnside initiated the study of representation theory, matrix algebra has played a central role with the indispensable idea of a group character [16]. Recently, point groups and crystallographic groups have been studied in geometric algebra [37, 40]. In this chapter, representations of the symmetric group are studied in the geometric algebra $${\mathbb{G}}_{n,n}$$ of neutral signature. The representation depends heavily upon the definition of a new twisted symmetric product, which does not depend upon a matrix representation, although it is equivalent to it.

Keywords: Symmetric Group; Geometric Algebra; Indispensable Idea; Neutral Signature; Twisted Product (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-0-8176-8385-6_12

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