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arXiv · 2506.06951

RSK correspondence for King tableaux with Berele insertion

Masato Kobayashi·Tomoo Matsumura
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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 $Q$-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.

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Masato Kobayashi, Tomoo Matsumura. 2026-02-27. RSK correspondence for King tableaux with Berele insertion. https://arxiv.org/abs/2506.06951

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