Abstract
For each integer m, Rasala [6] has shown how to list all the ordinary irreducible representations of the symmetric group n which have degree less than nm, provided that n is large enough, and in this note we shall prove similar results for the irreducible representations of n over an arbitrary field K. Our estimates are very crude, so although we recover Rasala's results, we get nowhere near his precise information on how large n has to be.
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