The Topology of the Unitary Dual of Crystallography Groups

2024/11/30 by Chan, Frankie, Weld, Ellen
#FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2412.00583

Abstract

We provide a procedure for generating the irreducible representations of crystallography groups in any dimension. We also furnish a strategy to investigate the topology of the unitary dual of a crystallography group using sequences of matrices. All irreducible representations (up to unitary equivalence) of the dimension 3 crystallography group 90 and some calculations involving sequences of these irreducible representations are included as a proof of concept of this procedure and strategy.

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