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Bibliographic Details
Main Author: Syed, Tariq
Format: Preprint
Published: 2020
Subjects:
Online Access:https://arxiv.org/abs/2010.06669
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Table of Contents:
  • For a smooth affine algebra $R$ of dimension $d \geq 3$ over a field $k$ and an invertible alternating matrix $χ$ of rank $2n$, the group $Sp(χ)$ of invertible matrices of rank $2n$ over $R$ which are symplectic with respect to $χ$ acts on the right on the set $Um_{2n}(R)$ of unimodular rows of length $2n$ over $R$. In this paper, we prove that $Sp(χ)$ acts transitively on $Um_{2n}(R)$ if $k$ is algebraically closed, $d! \in k^{\times}$ and $2n \geq d$.