Semi-magic matrices for dihedral groups

2021/10/27 by Donley, Robert W.
#15B51 (Primary) 05A05 05E18 20C05 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2110.14487

Abstract

After reviewing the group structure and representation theory for the dihedral group D_2n, we consider an intertwining operator Φ_ρ from the group algebra ℂ[D_2n] into a corresponding space of semi-magic matrices. From this intertwining operator, one obtains the generating function for enumerating the associated semi-magic squares with fixed line sum and an algebra extending the circulant matrices. While this work complements the approach to D_2n through permutation polytopes, we use only methods from representation theory.

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