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arXiv · 2309.07972

Witt invariants of Weyl groups

Tamar Blanks
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Abstract

We describe the Witt invariants of a Weyl group over a field $k_0$ by giving generators for the $W(k_0)$-module of Witt invariants, under the assumption that the characteristic of $k_0$ does not divide the order of the group. For the Weyl groups of types $B_n$, $C_n$, $D_n$, and $G_2$, we show that the Witt invariants are generated as a $W(k_0)$-algebra by trace forms and their exterior powers, extending a result due to Serre in type $A_n$. Many of our computational methods are applicable to computing Witt invariants of any smooth linear algebraic group over $k_0$, including a technique for lifting module generators from cohomological invariants to Witt invariants.

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Tamar Blanks. 2023-09-14. Witt invariants of Weyl groups. https://doi.org/10.1016/j.jalgebra.2024.07.029

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