  We show how the knowledge of the Fourier coefficients of the Cherednik kernel
leads to combinatorial formulas for generalized exponents. We recover known
formulas for generalized exponents of irreducible representations parameterized
by dominant roots, and obtain new formulas for the generalized exponents for
irreducible representations parameterized by the dominant elements of the root
lattice which are sums of two orthogonal short roots.
