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arXiv · 2407.14293

The multiplicative structure of the K-theoretical McKay correspondence for the Hilbert scheme of points in the complex plane

Jakub Koncki·Magdalena Zielenkiewicz
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Abstract

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 $\Lambda^n$. We prove a formula conjectured by Boissi\`ere for the endomorphism of $\Lambda^n$ induced by multiplication by the classes of the Adams powers of the tautological bundle. We describe the structure constants for the multiplication on $\Lambda^n$ induced by the tensor product in K-theory.

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Jakub Koncki, Magdalena Zielenkiewicz. 2024-07-19. The multiplicative structure of the K-theoretical McKay correspondence for the Hilbert scheme of points in the complex plane. https://arxiv.org/abs/2407.14293

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