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- W4287168049 abstract "Let $G$ be an algebraic group. For $dgeq 1$, we define the commuting probabilities $cp_d(G) = frac{dim(mathfrak C_d(G))}{dim(G^d)}$, where $mathfrak C_d(G)$ is the variety of commuting $d$-tuples in $G$. We prove that for a reductive group $G$ when $d$ is large, $cp_d(G)sim frac{alpha}{n}$ where $n=dim(G)$, and $alpha$ is the maximal dimension of an Abelian subgroup of $G$. For a finite reductive group $G$ defined over the field $mathbb F_q$, we show that $cp_{d+1}(G(mathbb F_q))sim q^{(alpha-n)d}$, and give several examples." @default.
- W4287168049 created "2022-07-25" @default.
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- W4287168049 date "2021-05-26" @default.
- W4287168049 modified "2023-10-17" @default.
- W4287168049 title "Asymptotics of commuting probabilities in reductive algebraic groups" @default.
- W4287168049 doi "https://doi.org/10.48550/arxiv.2105.12930" @default.
- W4287168049 hasPublicationYear "2021" @default.
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