Symplectic orbits of unimodular rows

Tariq Syed

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arXiv · 2010.06669

Symplectic orbits of unimodular rows

Tariq Syed

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Abstract

For a smooth affine algebra $R$ of dimension $d \geq 3$ over a field $k$ and an invertible alternating matrix $\chi$ of rank $2n$, the group $Sp(\chi)$ of invertible matrices of rank $2n$ over $R$ which are symplectic with respect to $\chi$ acts on the right on the set $Um_{2n}(R)$ of unimodular rows of length $2n$ over $R$. In this paper, we prove that $Sp(\chi)$ acts transitively on $Um_{2n}(R)$ if $k$ is algebraically closed, $d! \in k^{\times}$ and $2n \geq d$.

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Tariq Syed. 2020-10-13. Symplectic orbits of unimodular rows. https://arxiv.org/abs/2010.06669

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