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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 SL₂, 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 SL₂, 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.