Shifted twisted Yangians of quasi-split ADE types
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918260621967360 |
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| author | Lu, Kang Wang, Weiqiang Weekes, Alex |
| author_facet | Lu, Kang Wang, Weiqiang Weekes, Alex |
| contents | Associated to all quasi-split Satake diagrams of type ADE and even spherical coweights $μ$, we introduce the shifted iYangians ${}^\imath Y_μ$ and establish their PBW bases. We construct the iGKLO representations of ${}^\imath Y_μ$, which factor through quotients called truncated shifted iYangians ${}^\imath Y_μ^λ$. In type AI with $μ$ dominant, a variant of ${}^\imath Y_μ^{N\varpi_1^\vee}$ is identified with the truncated shifted iYangians in another definition, which are isomorphic to finite W-algebras of type BCD. These new family of algebras has connections and applications to fixed point loci of affine Grassmannian slices which will be developed in a sequel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19998 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shifted twisted Yangians of quasi-split ADE types Lu, Kang Wang, Weiqiang Weekes, Alex Representation Theory Quantum Algebra Associated to all quasi-split Satake diagrams of type ADE and even spherical coweights $μ$, we introduce the shifted iYangians ${}^\imath Y_μ$ and establish their PBW bases. We construct the iGKLO representations of ${}^\imath Y_μ$, which factor through quotients called truncated shifted iYangians ${}^\imath Y_μ^λ$. In type AI with $μ$ dominant, a variant of ${}^\imath Y_μ^{N\varpi_1^\vee}$ is identified with the truncated shifted iYangians in another definition, which are isomorphic to finite W-algebras of type BCD. These new family of algebras has connections and applications to fixed point loci of affine Grassmannian slices which will be developed in a sequel. |
| title | Shifted twisted Yangians of quasi-split ADE types |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2512.19998 |