Moduli space of homologically trivial parabolic (Higgs) bundles on the projective line and applications
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866918295552131072 |
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| author | Wen, Xueqing |
| author_facet | Wen, Xueqing |
| contents | We establish an isomorphism between the moduli space of homologically trivial parabolic (Higgs) bundles on $\mathbb{P}^1$ and the quiver variety associated to a star-shaped quiver. As applications, we deduce a closed formula for the Littlewood-Richardson coefficients from the Verlinde formula, and solve the nilpotent case of the Deligne-Simpson problem via geometric methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_01913 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Moduli space of homologically trivial parabolic (Higgs) bundles on the projective line and applications Wen, Xueqing Algebraic Geometry We establish an isomorphism between the moduli space of homologically trivial parabolic (Higgs) bundles on $\mathbb{P}^1$ and the quiver variety associated to a star-shaped quiver. As applications, we deduce a closed formula for the Littlewood-Richardson coefficients from the Verlinde formula, and solve the nilpotent case of the Deligne-Simpson problem via geometric methods. |
| title | Moduli space of homologically trivial parabolic (Higgs) bundles on the projective line and applications |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2101.01913 |