On the spinor norm in the unitary groups

zbMATH Open1425.11066arXiv1612.01218MaRDI QIDQ5235936

Ngo van Dinh

Publication date: 14 October 2019

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 $h$.

Full work available at URL: https://arxiv.org/abs/1612.01218

zbMATH Keywords

unitary groupspinor normspin groupsupercuspidal representation

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50) Classical groups (11E57)

Related Items (2)

Groups, Discriminants and the Spinor Norm ⋮ On the unitary dual of 𝑆𝑝𝑖𝑛(2𝑛,ℂ)

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