  For Iwahori-spherical representations of non-Archimedean general linear
groups, Chan-Savin recently expressed the Whittaker functor as a restriction to
an isotypic component of a finite Iwahori-Hecke algebra module. We generalize
this method to describe principal degenerate Whittaker functors. Concurrently,
we view Murnaghan's formula for the Harish-Chandra--Howe character as a
Grothendieck group expansion of the same module.
  Comparing the two approaches through the lens of Zelevinsky's PSH-algebras,
we obtain an explicit unitriangular transition matrix between coefficients of
the character expansion and the principal degenerate Whittaker dimensions.
