Geometric Construction of the McKay-Slodowy Correspondence
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918496233848832 |
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| author | Hou, Shengyu |
| author_facet | Hou, Shengyu |
| contents | This paper presents a geometric construction of the McKay-Slodowy correspondence, which extends the classical McKay correspondence. The classical McKay correspondence says: for a finite subgroup G of SL_2(C), there is a bijection between the set of nontrivial irreducible representations of G and the irreducible components of the exceptional locus of the minimal resolution of the quotient variety C^2/G. We generalizes it to a pair of groups: when G is a finite subgroup of SL_2(C) with a normal subgroup H, the set of induced nontrivial irreducible representations from H to G corresponds one-to-one to the set of pushing-forward of components of the exceptional locus of the minimal resolution of C^2/H under the quotient by G/H-action. Our proof is not given by case-by-case verification. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_11472 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric Construction of the McKay-Slodowy Correspondence Hou, Shengyu Algebraic Geometry 14E16 (Primary) 20C15 (Secondary) This paper presents a geometric construction of the McKay-Slodowy correspondence, which extends the classical McKay correspondence. The classical McKay correspondence says: for a finite subgroup G of SL_2(C), there is a bijection between the set of nontrivial irreducible representations of G and the irreducible components of the exceptional locus of the minimal resolution of the quotient variety C^2/G. We generalizes it to a pair of groups: when G is a finite subgroup of SL_2(C) with a normal subgroup H, the set of induced nontrivial irreducible representations from H to G corresponds one-to-one to the set of pushing-forward of components of the exceptional locus of the minimal resolution of C^2/H under the quotient by G/H-action. Our proof is not given by case-by-case verification. |
| title | Geometric Construction of the McKay-Slodowy Correspondence |
| topic | Algebraic Geometry 14E16 (Primary) 20C15 (Secondary) |
| url | https://arxiv.org/abs/2605.11472 |