Let G be a group and K a fields of characteristic 0. Let f be an element of the group algebra K[G]. Let X(f) be the matrix of the left-multiplication action of f on K[G]. We determine the eigenvalues and their multiplicities of X(f) when f is a central element of G, when f is an element of the descent algebra of K[G] for a coxeter group G, and when f is a special element of K[G] for a symmetric group G.
Randriamaro, Hery (021654868): Diagonalizability of elements of a group algebra. : Philipps-Universität Marburg 2012-05-18. DOI: https://doi.org/10.17192/z2012.0468.
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