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We determine the dimension of every simple module for the algebra of themonoid of all relations on a finite set (i.e. Boolean matrices). This is infact the same question as the determination of the dimension of everyevaluation of a simple correspondence functor. The method uses the theory ofsuch functors developed in [BT2, BT3], as well as some new ingredients in thetheory of finite lattices.

The algebra of Boolean matrices, correspondence functors, and simplicity