Work

RSK as a linear operator

Year: 2026

Type: article

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 .

Source: Selecta Mathematica

DOI: 10.1007/s00029-026-01191-5

Authors: Ada Stelzer, Alexander Yong

Institution: University of Illinois Urbana-Champaign

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: National Science Foundation, University of Illinois at Urbana-Champaign