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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2019
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/1905.01810 |
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| _version_ | 1866929760090718208 |
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| author | Mirkovic, Ivan Vybornov, Maxim |
| author_facet | Mirkovic, Ivan Vybornov, Maxim |
| contents | In type A we find equivalences of geometries arising in three settings: Nakajima's (``framed'') quiver varieties, conjugacy classes of matrices and loop Grassmannians. These are now all given by explicit formulas. In particular, we embedd the framed quiver varieties into Beilinson-Drinfeld Grassmannians. This provides a compactification of Nakajima varieties and a decomposition of affine Grassmannians into Nakajima varieties. As an application we provide a geometric version of symmetric and skew $(GL(m), GL(n))$ dualities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_01810 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Comparison of quiver varieties, loop Grassmannians and nilpotent cones in type A Mirkovic, Ivan Vybornov, Maxim Representation Theory 14L99, 22E57 In type A we find equivalences of geometries arising in three settings: Nakajima's (``framed'') quiver varieties, conjugacy classes of matrices and loop Grassmannians. These are now all given by explicit formulas. In particular, we embedd the framed quiver varieties into Beilinson-Drinfeld Grassmannians. This provides a compactification of Nakajima varieties and a decomposition of affine Grassmannians into Nakajima varieties. As an application we provide a geometric version of symmetric and skew $(GL(m), GL(n))$ dualities. |
| title | Comparison of quiver varieties, loop Grassmannians and nilpotent cones in type A |
| topic | Representation Theory 14L99, 22E57 |
| url | https://arxiv.org/abs/1905.01810 |