Finite local systems in the Drinfeld-Laumon construction

We calculate the result of a certain number of steps of the Drinfeld-Laumon construction (when a curve is a projective line) applied to a direct summand of the Springer-Laumon sheaf corresponding to any Young diagram, where the number of steps depends on the diagram and does not exceed the number of rows of the diagram. For smooth projective curves of positive genus we calculate the result of one step of the Drinfeld-Laumon construction (i.e. the Fourier-Deligne transform) when the length of the longest row of the Young diagram exceeds half of the content of the diagram. The result of the Drinfeld-Laumon construction is supported on a Harder-Narasimhan stratum, which in the case of one step can be expressed in terms of secant varieties of a curve in projective space.