On Relatively Projective Modules and the Külshammer–Robinson Basis

Abstract In this paper, we rewrite the relations between the Kulshammer–Robinson basis and Navarro basis in the local blocks, under Brauer correspondence. We define N-numbers and KR-matrix, then prove that they can be decided by decomposition numbers and Cartan matrix of local blocks. We give explicit connections between Kulshammer–Robinson basis and projective modules. For N-blocks, we give other ways to describe the connections.