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arXiv · 2509.00853

Berele row-insertion and quantum symmetric pairs

Hideya Watanabe
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Abstract

The Berele row-insertion is a symplectic analogue of the Schensted row-insertion. In the present paper, we provide it with a representation theoretical interpretation via the quantum symmetric pairs of type $A\mathrm{II}$. As applications, we lift Berele's Robinson--Schensted correspondence and Kobayashi--Matsumura's Robinson--Schensted--Knuth (RSK for short) correspondence to isomorphisms of representations over a quantum symmetric pair coideal subalgebra, and establish the dual RSK correspondence of type $A\mathrm{II}$.

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Hideya Watanabe. 2025-08-31. Berele row-insertion and quantum symmetric pairs. https://arxiv.org/abs/2509.00853

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