Relative Frobenius formula

Abstract

For a finite group [Formula: see text], Frobenius found a formula for the values of the function [Formula: see text] for even integers [Formula: see text], where [Formula: see text] is the set of irreducible representations of [Formula: see text]. We generalize this formula to the relative case: for a subgroup [Formula: see text], we find a formula for the values of the function [Formula: see text]. We apply our results to compute the E-polynomials of Fock–Goncharov spaces and to relate the Gelfand property to the geometry of generalized Fock–Goncharov spaces.