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arXiv · 1612.01218

On the spinor norm in the unitary groups

Ngo Van Dinh
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Abstract

Let $F$ be a field of odd characteristic, $E$ be a finite extension of $F$ equipped an involution with subfield of fixed points $E_0$ containing $F$ and $V$ be a finite dimensional $E$-vector space with a non-degenerate hermitian form $h$. We show a link between the spinor norm in the unitary group $U(V,h)$ and the calculus of determinants and discriminants. Then we show a formula which links the spinor norm in $U(V,h)$ and the spinor norm in the orthogonal group $O(V,b_h)$ defined by a non-degenerate symmetric bilinear form $b_h$ associated to $h$.

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Ngo Van Dinh. 2016-12-05. On the spinor norm in the unitary groups. https://arxiv.org/abs/1612.01218

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