Instantons on ALE spaces for classical groups, involutions on quiver varieties, and quantum symmetric pairs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918161510563840 |
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| author | Nakajima, Hiraku |
| author_facet | Nakajima, Hiraku |
| contents | Moduli spaces of instantons on ALE spaces for classical groups are examples of fixed point sets of involutions on quiver varieties, i.e., $σ$-quiver varieties. In 2018 Yiqiang Li considered their equivariant cohomology, and by stable envelope of Maulik-Okounkov, constructed representations of coideal subalgebras of Maulik-Okounkov Yangian, called twisted Yangian. We calculate $K$-matrices as matrices in examples, identified the twisted Yangians with ones studied in other literature, and clarify conditions which we should impose to make them well-defined. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_13007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Instantons on ALE spaces for classical groups, involutions on quiver varieties, and quantum symmetric pairs Nakajima, Hiraku Representation Theory High Energy Physics - Theory Algebraic Geometry Quantum Algebra Moduli spaces of instantons on ALE spaces for classical groups are examples of fixed point sets of involutions on quiver varieties, i.e., $σ$-quiver varieties. In 2018 Yiqiang Li considered their equivariant cohomology, and by stable envelope of Maulik-Okounkov, constructed representations of coideal subalgebras of Maulik-Okounkov Yangian, called twisted Yangian. We calculate $K$-matrices as matrices in examples, identified the twisted Yangians with ones studied in other literature, and clarify conditions which we should impose to make them well-defined. |
| title | Instantons on ALE spaces for classical groups, involutions on quiver varieties, and quantum symmetric pairs |
| topic | Representation Theory High Energy Physics - Theory Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2510.13007 |