Spinorial Representations of Symmetric Groups

2019/06/18 by Ganguly, Jyotirmoy, Spallone, Steven · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1906.07481

Abstract

A real representation π of a finite group may be regarded as a homomorphism to an orthogonal group \Or(V). For symmetric groups S_n, alternating groups A_n, and products S_n × S_n' of symmetric groups, we give criteria for whether π lifts to the double cover \Pin(V) of \Or(V), in terms of character values. From these criteria, we compute the second Stiefel-Whitney classes of these representations.

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