Abstract
We describe a basis of the center of the Schur algebra that comes from conjugacy classes in the symmetric group via Schur–Weyl duality. We give a combinatorial description of expansions of these basis elements in terms of the basis originally used by Schur. The primitive central idempotents of the Schur algebra can be written down using this basis and the character table of the symmetric group in the semisimple case. Along the way we prove a result on the non-singularity of the submatrix of the character table matrix of a symmetric group obtained by taking rows and columns indexed by partitions with at most [Formula: see text] parts for any [Formula: see text].
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