Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929255313571840 |
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| author | Chen, Xiaojun He, Weiqiang Yu, Sirui |
| author_facet | Chen, Xiaojun He, Weiqiang Yu, Sirui |
| contents | We show that the specialized quantum D-module of the equivariant quantum cohomology ring of the minimal resolution of an ADE singularity is isomorphic to the D-module of graded traces on the minimal nilpotent orbit in the Lie algebra of the same type. This generalizes a recent result of Shlykov [Hikita conjecture for the minimal nilpotent orbit, to appear in Proc. AMS, https://doi.org/10.1090/proc/15281] and hence verifies in this case the quantum version of Hikita's conjecture, proposed by Kamnitzer, McBreen and Proudfoot [The quantum Hikita conjecture, Advances in Mathematics 390 (2021) 107947]. We also show analogous isomorphisms for singularities of BCFG type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_13249 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture Chen, Xiaojun He, Weiqiang Yu, Sirui Representation Theory Algebraic Geometry We show that the specialized quantum D-module of the equivariant quantum cohomology ring of the minimal resolution of an ADE singularity is isomorphic to the D-module of graded traces on the minimal nilpotent orbit in the Lie algebra of the same type. This generalizes a recent result of Shlykov [Hikita conjecture for the minimal nilpotent orbit, to appear in Proc. AMS, https://doi.org/10.1090/proc/15281] and hence verifies in this case the quantum version of Hikita's conjecture, proposed by Kamnitzer, McBreen and Proudfoot [The quantum Hikita conjecture, Advances in Mathematics 390 (2021) 107947]. We also show analogous isomorphisms for singularities of BCFG type. |
| title | Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2302.13249 |