K-theoretic Hikita conjecture for quiver gauge theories
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911356124397568 |
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| author | Dumanski, Ilya Krylov, Vasily |
| author_facet | Dumanski, Ilya Krylov, Vasily |
| contents | We study variants of Hikita conjecture for Nakajima quiver varieties and corresponding Coulomb branches. First, we derive the equivariant version of the conjecture from the non-equivariant one for a set of gauge theories. Second, we suggest a variant of the conjecture, with K-theoretic Coulomb branches involved. We show that this version follows from the usual (homological) one for a set of theories. We apply this result to prove the conjecture in finite ADE types. In the course of the proof, we show that appropriate completions of K-theoretic and homological (quantized) Coulomb branches are isomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06226 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | K-theoretic Hikita conjecture for quiver gauge theories Dumanski, Ilya Krylov, Vasily Representation Theory Mathematical Physics K-Theory and Homology We study variants of Hikita conjecture for Nakajima quiver varieties and corresponding Coulomb branches. First, we derive the equivariant version of the conjecture from the non-equivariant one for a set of gauge theories. Second, we suggest a variant of the conjecture, with K-theoretic Coulomb branches involved. We show that this version follows from the usual (homological) one for a set of theories. We apply this result to prove the conjecture in finite ADE types. In the course of the proof, we show that appropriate completions of K-theoretic and homological (quantized) Coulomb branches are isomorphic. |
| title | K-theoretic Hikita conjecture for quiver gauge theories |
| topic | Representation Theory Mathematical Physics K-Theory and Homology |
| url | https://arxiv.org/abs/2509.06226 |