Shifted twisted Yangians and affine Grassmannian islices
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914218241949696 |
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| author | Lu, Kang Wang, Weiqiang Weekes, Alex |
| author_facet | Lu, Kang Wang, Weiqiang Weekes, Alex |
| contents | In a prequel we introduced the shifted iYangians ${}^\imath Y_μ$ associated to quasi-split Satake diagrams of type ADE and even spherical coweights $μ$, and constructed the iGKLO representations of ${}^\imath Y_μ$, which factor through truncated shifted iYangians ${}^\imath Y_μ^λ$. In this paper, we show that ${}^\imath Y_μ$ quantizes the involutive fixed point locus ${}^\imath W_μ$ arising from affine Grassmannians of type ADE, and supply strong evidence toward the expectation that ${}^\imath Y_μ^λ$ quantizes a top-dimensional component of the affine Grassmannian islice ${}^\imath\overline{W}_μ^λ$. We identify the islices ${}^\imath\overline{W}_μ^λ$ in type AI with suitable nilpotent Slodowy slices of type BCD, building on the work of Lusztig and Mirković-Vybornov in type A. We propose a framework for producing ortho-symplectic (and hybrid) Coulomb branches from split (and nonsplit) Satake framed double quivers, which are conjectured to relate closely to the islices ${}^\imath\overline{W}_μ^λ$ and the algebras ${}^\imath Y_μ^λ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10652 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shifted twisted Yangians and affine Grassmannian islices Lu, Kang Wang, Weiqiang Weekes, Alex Representation Theory Algebraic Geometry Quantum Algebra In a prequel we introduced the shifted iYangians ${}^\imath Y_μ$ associated to quasi-split Satake diagrams of type ADE and even spherical coweights $μ$, and constructed the iGKLO representations of ${}^\imath Y_μ$, which factor through truncated shifted iYangians ${}^\imath Y_μ^λ$. In this paper, we show that ${}^\imath Y_μ$ quantizes the involutive fixed point locus ${}^\imath W_μ$ arising from affine Grassmannians of type ADE, and supply strong evidence toward the expectation that ${}^\imath Y_μ^λ$ quantizes a top-dimensional component of the affine Grassmannian islice ${}^\imath\overline{W}_μ^λ$. We identify the islices ${}^\imath\overline{W}_μ^λ$ in type AI with suitable nilpotent Slodowy slices of type BCD, building on the work of Lusztig and Mirković-Vybornov in type A. We propose a framework for producing ortho-symplectic (and hybrid) Coulomb branches from split (and nonsplit) Satake framed double quivers, which are conjectured to relate closely to the islices ${}^\imath\overline{W}_μ^λ$ and the algebras ${}^\imath Y_μ^λ$. |
| title | Shifted twisted Yangians and affine Grassmannian islices |
| topic | Representation Theory Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2510.10652 |