The action of the Murphy element on the restricition of an irreducible Sn-Module to Sn-1
Ellers, Harald and Murray, John (2007) The action of the Murphy element on the restricition of an irreducible Sn-Module to Sn-1. Preprint . pp. 1-21.
We study the irreducible representations of the symmetric group n over a eld F of positive characteristic p. For convenience, but no loss of generality, we shall assume that F is algebraically closed. Let = (1 2 : : : l > 0) be a partition of n. As usual the set of nodes  := f(i; j) 2 Z2 j 1 i l; 1 j ig is called the Young diagram of . We represent  as a set of square boxes in Z2, by placing a square with opposite corners (i 1; j 1) and (i; j), for each (i; j) 2 . In accordance with the anglo-american convention, we orient the positive direction of the Y -axis downwards. The transpose 0 of is the partition of n dened by 0 i = #fj j j ig, for all i. The Young diagram of 0 is obtained from  by re ection in the main diagonal.
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