The classification of spinors under 𝐺𝑆𝑝𝑖𝑛₁₄ over finite fields

Zhu, Xiao-Wei

doi:10.1090/S0002-9947-1992-1102227-2

The classification of spinors under $\textrm {GSpin}_ {14}$ over finite fields
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Trans. Amer. Math. Soc. 333 (1992), 95-114 Request permission

Abstract:

The spinors of a $14$-dimensional vector space $V$ are studied with respect to the group $\operatorname {GSpin}_{14}$ of the $14$-dimensional vector space $V$ over finite fields ${{\mathbf {F}}_q}$. Results are given as follows: (1) the decomposition of the space of spinors into $\operatorname {GSpin}_{14}$-equivalence classes or "orbits" over ${{\mathbf {F}}_q}$, (2) the structure of the fixer of $\operatorname {GSpin}_{14}$ for each orbit as an ${{\mathbf {F}}_q}$-group.

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