RSK correspondence for King tableaux with Berele insertion
Combinatorics
2026-03-02 v2
Abstract
We establish a bijective RSK correspondence of type C for King tableaux with Berele insertion as a reformulation of Sundaram's correspondence (1986). For its -symbol, we make use of semistandard oscillating tableaux (SSOT), a new object which Lee (2025) introduced. Further, we show hidden duality of Cauchy identity through RSK correspondences of type A and C. Finally, we prove that the generating function of SSOT is symmetric by constructing a new sort of Bender-Knuth involution.
Cite
@article{arxiv.2506.06951,
title = {RSK correspondence for King tableaux with Berele insertion},
author = {Masato Kobayashi and Tomoo Matsumura},
journal= {arXiv preprint arXiv:2506.06951},
year = {2026}
}
Comments
22 pages. In version 2, we fixed the statement and proof of Theorem 4.17