Geodesic
Elementary covering numbers in odd-dimensional unitary groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 37, Tome 500 (2021), pp. 158-176 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $(K,\Delta)$ be a Hermitian form field and $n\geq 3$. We prove that if $\sigma\in \mathrm{U}_{2n+1}(K,\Delta)$ is a unitary matrix of level $(K,\Delta)$, then any short root transvection $T_{ij}(x)$ is a product of $4$ elementary unitary conjugates of $\sigma$ and $\sigma^{-1}$. Moreover, the bound $4$ is sharp. We also show that any extra short root transvection $T_i(x,y)$ is a product of $12$ elementary unitary conjugates of $\sigma$ and $\sigma^{-1}$. If the level of $\sigma$ is $(0,K\times 0)$, then any $(0,K\times 0)$-elementary extra short root transvection $T_i(x,0)$ is a product of $2$ elementary unitary conjugates of $\sigma$ and $\sigma^{-1}$. 
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     author = {R. Preusser},
     title = {Elementary covering numbers in odd-dimensional unitary groups},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_500_a7/}
}
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R. Preusser. Elementary covering numbers in odd-dimensional unitary groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 37, Tome 500 (2021), pp. 158-176. http://geodesic.mathdoc.fr/item/ZNSL_2021_500_a7/

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