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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.14293 |
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| _version_ | 1866910189833158656 |
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| author | Koncki, Jakub Zielenkiewicz, Magdalena |
| author_facet | Koncki, Jakub Zielenkiewicz, Magdalena |
| contents | We consider the K-theory of the Hilbert scheme of points in the complex plane, which under McKay correspondence is isomorphic to the space of symmetric functions $Λ^n$. We prove a formula conjectured by Boissière for the endomorphism of $Λ^n$ induced by multiplication by the classes of the Adams powers of the tautological bundle. We describe the structure constants for the multiplication on $Λ^n$ induced by the tensor product in K-theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14293 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The multiplicative structure of the K-theoretical McKay correspondence for the Hilbert scheme of points in the complex plane Koncki, Jakub Zielenkiewicz, Magdalena Algebraic Geometry 14C05 We consider the K-theory of the Hilbert scheme of points in the complex plane, which under McKay correspondence is isomorphic to the space of symmetric functions $Λ^n$. We prove a formula conjectured by Boissière for the endomorphism of $Λ^n$ induced by multiplication by the classes of the Adams powers of the tautological bundle. We describe the structure constants for the multiplication on $Λ^n$ induced by the tensor product in K-theory. |
| title | The multiplicative structure of the K-theoretical McKay correspondence for the Hilbert scheme of points in the complex plane |
| topic | Algebraic Geometry 14C05 |
| url | https://arxiv.org/abs/2407.14293 |