Loop Grassmannian of quivers and Compactified Coulomb branch of quiver gauge theory with no framing
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913465001574400 |
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| author | Dong, Zhijie |
| author_facet | Dong, Zhijie |
| contents | Mirković introduced the notion of loop Grassmannian for symmetric integer matrix $κ$. It is a two-step limit of the local projective space $Z_κ^α$, which generalizes the usual Zastava for a simply laced group $G$. The usual loop Grassmannian of $G$ is recovered when the matrix $κ$ is the Cartan matrix of $G$.
On the other hand, Braverman, Finkelberg, and Nakajima showed that the Compactified Coulomb branch $\mathbf{M}_{Q}^α$ for the quiver gauge theory with no framing also generalizes the usual Zastava. We show that in the case when $κ$ is the associated matrix of the quiver $Q$, these two generalizations of Zastava coincide, i.e $\mathbf{M}_{Q}^α\cong Z_{κ(Q)}^α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05458 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Loop Grassmannian of quivers and Compactified Coulomb branch of quiver gauge theory with no framing Dong, Zhijie Representation Theory Algebraic Geometry Mirković introduced the notion of loop Grassmannian for symmetric integer matrix $κ$. It is a two-step limit of the local projective space $Z_κ^α$, which generalizes the usual Zastava for a simply laced group $G$. The usual loop Grassmannian of $G$ is recovered when the matrix $κ$ is the Cartan matrix of $G$. On the other hand, Braverman, Finkelberg, and Nakajima showed that the Compactified Coulomb branch $\mathbf{M}_{Q}^α$ for the quiver gauge theory with no framing also generalizes the usual Zastava. We show that in the case when $κ$ is the associated matrix of the quiver $Q$, these two generalizations of Zastava coincide, i.e $\mathbf{M}_{Q}^α\cong Z_{κ(Q)}^α$. |
| title | Loop Grassmannian of quivers and Compactified Coulomb branch of quiver gauge theory with no framing |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2408.05458 |