  Let S_d be the symmetric group on d letters and let k be a field of
characteristic p>2. Tensoring an irreducible S_d module with the sign
representation defines an involution on the p-regular partitions of d. It is
suprisingly difficult to describe this involution combinatorially. Mullineux
conjectured an algorithmic description in 1979. Kleshchev gave an entirely new
algorithm describing the involution in 1996 and proved with Ford that it agrees
with Mullineux's. Using the modular representation theory of the supergroup
GL(m|n) we provide the first new proof of the Mullineux conjecture which is
independent of Kleshchev's approach. Similar techniques allow us to classify
the irreducible polynomial representations of GL(m|n), completing recent
partial results by Donkin.
