  This is the second paper in a sequence devoted to giving manifestly
non-negative formulas for generalized exponents of small representations in all
types. It contains a first formula for generalized exponents of small weights
which extends the Shapiro-Steinberg formula for classical exponents. The
formula is made possible by a computation of Fourier coefficients of the
degenerate Cherednik kernel. Unlike the usual partition function coefficients,
the answer reflects only the combinatorics of minimal expressions as a sum of
roots.
