Resumen de Cyclic groups with the same Hodge series

Daryl R. Deford, Peter G. Doyle

• 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.