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We study the existence of unitriangular basic sets for the symmetric groupwhich behave nicely with respect to the Mullineux involution. Such sets give anatural labelling for the modular irreducible representations. We show that,for any odd prime p, the p-blocks of the symmetric group with weight 2 havestable unitriangular basic sets which we describe by studying the combinatoricsof partitions in these blocks.

Unitriangular basic sets for blocks of the symmetric and alternating groups of small weights