General runner removal and the Mullineux map

Details General runner removal and the Mullineux map General runner removal and the Mullineux map

2007-12-14

arxiv.org/abs/0712.2390v8

J. Algebra 322 (2009) 4331-4367

Mathematics

Representation Theory

40 pages

Scientific paper

10.1016/j.jalgebra.2009.09.027

We prove a new `runner removal theorem' for $q$-decomposition numbers of the
level 1 Fock space of type $A^{(1)}_{e-1}$, generalising earlier theorems of
James--Mathas and the author. By combining this with another theorem relating
to the Mullineux map, we show that the problem of finding all $q$-decomposition
numbers indexed by partitions of a given weight is a finite computation.

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