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For Iwahori-spherical representations of non-Archimedean general lineargroups, Chan-Savin recently expressed the Whittaker functor as a restriction toan isotypic component of a finite Iwahori-Hecke algebra module. We generalizethis method to describe principal degenerate Whittaker functors. Concurrently,we view Murnaghan's formula for the Harish-Chandra--Howe character as aGrothendieck 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 ofthe character expansion and the principal degenerate Whittaker dimensions.

A triangular system for local character expansions of Iwahori-spherical representations of general linear groups