Witt invariants of Weyl groups

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.

21 pages. Lemma 3.5 was added to simplify the assumptions on $k_0$ in Theorems 5.4 and 5.6

References in corpus (1)

• Cohomological invariants mod 2 of Weyl groups