# Abstract

What happens if one tries to define a Springer correspondance using perverse
sheaves modulo l instead of perverse sheaves with characteristic zero
coefficients ? In the example of SL_{2}, one can determine the Loewy
structure of
the perverse sheaves involved, and make some conjectures about what should
hold
in general. In the case of SL_{2}, to involve all partitions of n, one is
tempted
to use a sum of induced representations which leads to the Schur algebra.
The
decomposition numbers for the Schur algebra and for the perverse shaves on
the
nilpotent variety form unitrangular matrices and are the same for adjacent
partitions! Conjecture : the two matrices are equal.