Differential operators on the base affine space of $SL_n$ and quantized Coulomb branches
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917216107102208 |
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| author | Gannon, Tom Williams, Harold |
| author_facet | Gannon, Tom Williams, Harold |
| contents | We show that the algebra $D_\hbar(SL_n/U)$ of differential operators on the base affine space of $SL_n$ is the quantized Coulomb branch of a certain 3d $\mathcal{N} = 4$ quiver gauge theory. In the semiclassical limit this proves a conjecture of Dancer-Hanany-Kirwan about the universal hyperkähler implosion of $SL_n$. We also formulate and prove a generalization identifying the Hamiltonian reduction of $T^* SL_n$ with respect to an arbitrary unipotent character as a Coulomb branch. As an application of our results, we provide a new interpretation of the Gelfand-Graev symmetric group action on $D_\hbar(SL_n/U)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10278 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Differential operators on the base affine space of $SL_n$ and quantized Coulomb branches Gannon, Tom Williams, Harold Representation Theory Mathematical Physics Algebraic Geometry We show that the algebra $D_\hbar(SL_n/U)$ of differential operators on the base affine space of $SL_n$ is the quantized Coulomb branch of a certain 3d $\mathcal{N} = 4$ quiver gauge theory. In the semiclassical limit this proves a conjecture of Dancer-Hanany-Kirwan about the universal hyperkähler implosion of $SL_n$. We also formulate and prove a generalization identifying the Hamiltonian reduction of $T^* SL_n$ with respect to an arbitrary unipotent character as a Coulomb branch. As an application of our results, we provide a new interpretation of the Gelfand-Graev symmetric group action on $D_\hbar(SL_n/U)$. |
| title | Differential operators on the base affine space of $SL_n$ and quantized Coulomb branches |
| topic | Representation Theory Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2312.10278 |