Grothendieck group of the stack of G-Zips

Simon Cooper

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arXiv · 2410.01547

Grothendieck group of the stack of G-Zips

Simon Cooper

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Abstract

Given a connected reductive group G over the finite field of order p and a cocharacter of G over the algebraic closure of the finite field, we can define G-Zips. The collection of these G-Zips form an algebraic stack which is a stack quotient of G. In this paper we study the K-theory rings of this quotient stack, focusing on the Grothendieck group. Under the additional assumption that the derived group is simply connected, the Grothendieck group is described as a quotient of the representation ring of the Levi subgroup centralising the cocharacter.

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Simon Cooper. 2024-10-02. Grothendieck group of the stack of G-Zips. https://arxiv.org/abs/2410.01547

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