Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

On the minimal dimensions of irreducible representations of symmetric groups

G. D. Jamesa1

a1 Sidney Sussex College, Cambridge

For each integer m, Rasala [6] has shown how to list all the ordinary irreducible representations of the symmetric group S0305004100000803xs1D516n 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 S0305004100000803xs1D516n 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.

(Received April 18 1983)