Revista de la
Unión Matemática Argentina
Cyclic groups with the same Hodge series
Daryl R. DeFord, Peter G. Doyle
Volume 59, no. 2 (2018), pp. 241–254


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The Hodge series of a finite matrix group is the generating function for invariant exterior forms of specified order $p$ and degree $k$. Lauret, Miatello, and Rossetti gave examples of pairs of non-conjugate cyclic groups having the same Hodge series; the corresponding space forms are isospectral for the Laplacian on $p$-forms for all $p$, but not for all natural operators. Here we explain, simplify, and extend their investigations.