Berele Row-Insertion and Quantum Symmetric Pairs

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 AII. 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 AII.