$K$-theoretic Coulomb branches of quiver gauge theories and cluster varieties
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866915708146810880 |
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| author | Schrader, Gus Shapiro, Alexander |
| author_facet | Schrader, Gus Shapiro, Alexander |
| contents | For $Γ$ a quiver without 1-cycles, we show that the Braverman--Finkelberg--Najakima quantized $K$-theoretic Coulomb branch algebra $\mathscr{A}_Γ$ of the corresponding quiver gauge theory is isomorphic to the quantized universally Laurent algebra (upper cluster $X$-algebra) associated to an explicit initial seed $Π_Γ$. We also show that $Π_Γ$ admits a cluster Donaldson--Thomas transformation as defined by Keller. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_03186 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | $K$-theoretic Coulomb branches of quiver gauge theories and cluster varieties Schrader, Gus Shapiro, Alexander Quantum Algebra Mathematical Physics Representation Theory For $Γ$ a quiver without 1-cycles, we show that the Braverman--Finkelberg--Najakima quantized $K$-theoretic Coulomb branch algebra $\mathscr{A}_Γ$ of the corresponding quiver gauge theory is isomorphic to the quantized universally Laurent algebra (upper cluster $X$-algebra) associated to an explicit initial seed $Π_Γ$. We also show that $Π_Γ$ admits a cluster Donaldson--Thomas transformation as defined by Keller. |
| title | $K$-theoretic Coulomb branches of quiver gauge theories and cluster varieties |
| topic | Quantum Algebra Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/1910.03186 |