This talk is based on my collaboration with
Tsuchioka, Kreiman and Jacon. In the first half,
I explain a path model realization of level
one crystals of $\mathfrak g(A^{(1)}_{e-1})$ in
terms of sequences of partitions. In the second half,
I explain its applications. The first is description of
the famous Mullineux map. (This new description was a
result of my conversation with Fayers in Oberwolfach some
years ago.) The second is confirmation of a conjecture
by Dipper, James and Murphy.

Lecture #12686

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