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The problem of source algebra equivalences between blocks at the ends of themaximal strings of spin blocks of the symmetric and alternating groups hasrecently been settled, but so far there has not even been a candidate of thetilting complex defining the reflections of the internal blocks of the string.Our aim in this paper is to propose a definition for the mappings E_i and F_iand for their divided powers. The solution we propose here is to halve theoperators only when both halves are isomorphic, which, on the level of theGrothendieck group, corresponds to working with paired simples as pairs, andcrossing over between the symmetric and alternating groups, in order to sendpaired simples to paired simples.This is equivalent to working with theirreducible supermodules, as in the work of Brundan and Kleshchev, though wedon't introduce the supermodule language into this paper. The main differencebetween our approach and theirs is the crossovers, which occasionally forceextra halving of modules.The definition is based on the method of permutation modules from Kessar-Schaps. We apply it to short strings and show that, at leaston the individual strings, it is compatible with the form of the tiltingcomplex used by Chuang and Rouquier.

sl_2-actions along short strings for spin blocks