相关论文: Cohomological invariants mod 2 of Weyl groups

In a previous paper, we showed that all the cohomological invariants of Weyl groups are completely determined by their restrictions to the abelian subgroups generated by reflections. Using this principle, we describe all the cohomological…

We determine the cohomological invariants and the Witt invariants of the alternating group $A_n$.

In this note, we show the polynomiality of the ring of invariants with respect to the Weyl group of type $A_{2l}^{(2)}$.

We calculate the Weyl group invariants with respect to a maximal torus of the exceptional Lie group $E_6$.

We determine the mod p cohomological invariants for several affine group schemes G in chararacteristic p. These are invariants of G-torsors with values in etale motivic cohomology, or equivalently in Kato's version of Galois cohomology…

We compute the invariants so of Weyl groups in mod 2 Milnor K-theory and more general cycle modules, which are annihilated by 2. Over a base field of characteristic coprime to the group order, the invariants decompose as direct sums of the…

In this paper, we generalize Serre's splitting theorem for cohomological invariants of the symmetric group to finite Coxeter groups, provided that the ground field has characteristic zero. We then use this principle to determine all the…

Let F denote a field of characteristic different from two. In this paper we describe the mod 2 cohomology of a Galois group which is determined by the Witt ring WF.

We introduce geometric invariants for $p$-groups of class $2$ and exponent $p$. We report on their effectiveness in distinguishing among 5-generator $p$-groups of this type.

We show that the mod 2 Seiberg-Witten invariant can be determined for a spin manifold X which has the same homology groups as the 4-torus. The value depends on the structure of the cohomology ring of X, and in particular on the 4-fold cup…

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…

We describe the quantum cohomology rings of a class of toric varieties. The description includes, in addition to the (already known) ring presentations, the (new) analogues for toric varieties of the sorts of quantum Giambelli formulas…

In this paper we compute the mod 2 cohomology of the McLaughlin group, which is one of the sporadic simple groups.

The mod 2 cohomology algebra of the holomorph of any finite cyclic group whose order is a power of 2 is determined.

We define degree two cohomological invariants for G-Galois algebras over fields of characteristic not 2, and use them to give necessary conditions for the existence of a self--dual normal basis. In some cases, we show that these conditions…

For any odd prime $p$, we prove that the induced homomorphism from the mod $p$ cohomology of the classifying space of a compact simply-connected simple connected Lie group to the Weyl group invariants of the mod $p$ cohomology of the…

In this paper, we compute the $RO(\mathbb{Z}/2)$-graded equivariant cohomology of rotation groups and Stiefel manifolds with particular involutions.

We compute the cohomological invariants of $\mathcal{H}_g$, the moduli stack of smooth hyperelliptic curves, for every odd $g$.

Let G be a complex, connected, reductive algebraic group with Weyl group W and Steinberg variety Z. We show that the graded Borel-Moore homology of Z is isomorphic to the smash product of the coinvariant algebra of W and the group algebra…

We describe the ring of modular forms of degree 2 in characteristic 2 using its relation with curves of genus 2.