RSK as a linear operator
Rings and Algebras
2024-12-23 v2 Combinatorics
Representation Theory
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 classification of Dynkin diagrams, as well as the diagram for .
Cite
@article{arxiv.2410.23009,
title = {RSK as a linear operator},
author = {Ada Stelzer and Alexander Yong},
journal= {arXiv preprint arXiv:2410.23009},
year = {2024}
}
Comments
We thank S. Fomin for comments that led to a reformulation of the diagonalizability theorem in terms of Dynkin diagrams. 37 pages