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RSK as a linear operator (2410.23009v2)
Published 30 Oct 2024 in math.RA, math.CO, and math.RT
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 $E_9$.