Berele row-insertion and quantum symmetric pairs
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915493310365696 |
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| author | Watanabe, Hideya |
| author_facet | Watanabe, Hideya |
| contents | 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 $A\mathrm{II}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Berele row-insertion and quantum symmetric pairs Watanabe, Hideya Representation Theory Combinatorics Primary 17B37, Secondary 17B10, 05E10 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 $A\mathrm{II}$. |
| title | Berele row-insertion and quantum symmetric pairs |
| topic | Representation Theory Combinatorics Primary 17B37, Secondary 17B10, 05E10 |
| url | https://arxiv.org/abs/2509.00853 |