Two dimensional versions of the affine Grassmannian and their geometric description
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915850796138496 |
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| author | Maffei, Andrea Melani, Valerio Vezzosi, Gabriele |
| author_facet | Maffei, Andrea Melani, Valerio Vezzosi, Gabriele |
| contents | For a smooth affine algebraic group $G$ over an algebraically closed field, we consider several two-variables generalizations of the affine Grassmannian $G(\!(t)\!)/G[\![t]\!]$, given by quotients of the double loop group $G(\!(x)\!)(\!(y)\!)$. We prove that they are representable by ind-schemes if $G$ is solvable. Given a smooth surface $X$ and a flag of subschemes of $X$, we provide a geometric interpretation of the two-variables Grassmannians, in terms of bundles and trivialisation data defined on appropriate loci in $X$, which depend on the flag. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_16353 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two dimensional versions of the affine Grassmannian and their geometric description Maffei, Andrea Melani, Valerio Vezzosi, Gabriele Algebraic Geometry Representation Theory 14D23, 20G05, 18F20 For a smooth affine algebraic group $G$ over an algebraically closed field, we consider several two-variables generalizations of the affine Grassmannian $G(\!(t)\!)/G[\![t]\!]$, given by quotients of the double loop group $G(\!(x)\!)(\!(y)\!)$. We prove that they are representable by ind-schemes if $G$ is solvable. Given a smooth surface $X$ and a flag of subschemes of $X$, we provide a geometric interpretation of the two-variables Grassmannians, in terms of bundles and trivialisation data defined on appropriate loci in $X$, which depend on the flag. |
| title | Two dimensional versions of the affine Grassmannian and their geometric description |
| topic | Algebraic Geometry Representation Theory 14D23, 20G05, 18F20 |
| url | https://arxiv.org/abs/2503.16353 |