RSK as a linear operator

Abstract

Abstract The Robinson–Schensted–Knuth correspondence (RSK) is a bijection between nonnegative integer matrices and pairs of Young tableaux. We study it as a linear operator on the coordinate ring of matrices, proving results about its diagonalizability, eigenvalues, trace, and determinant. Our criterion for diagonalizability involves the ADE classification of Dynkin diagrams, as well as the diagram for $$E_9$$ E 9 .