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arXiv · 2604.21738

On the induction functor from group algebras to distribution algebras

Christopher P. Bendel·Daniel K. Nakano·Cornelius Pillen
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Abstract

Let $G$ be a reductive algebraic group scheme defined over ${\mathbb F}_{p}$ and $k$ be an algebraically closed field of characteristic $p$. There are two associated families of finite group schemes, the $r$-th Frobenius kernels, denoted by $G_r$, and the fixed points of the iterated Frobenius map, the finite groups of Lie type, denoted by $G(\mathbb{F}_q).$ Bendel, Nakano and Pillen initiated the investigation of the induction functor $\operatorname{ind}_{G(\mathbb{F}_q)}^G-$. Using filtrations and truncation, large amounts of data coming from the algebraic group and the Frobenius kernels can be transferred to the finite group. This paper looks at connections between a fundamental theorem of Chastkofsky and Jantzen and the induction functor via the cohomology and representation theory of $G$.

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Christopher P. Bendel, Daniel K. Nakano, Cornelius Pillen. 2026-04-23. On the induction functor from group algebras to distribution algebras. https://arxiv.org/abs/2604.21738

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