Natural projectors in tensor spaces.
Let be a field, G a reductive algebraic -group, and G 1 ≤ G a reductive subgroup. For G 1 ≤ G, the corresponding groups of -points, we study the normalizer N = N G(G 1). In particular, for a standard embedding of the odd orthogonal group G 1 = SO(m, ) in G = SL(m, ) we have N ≅ G 1 ⋊ µm(), the semidirect product of G 1 by the group of m-th roots of unity in . The normalizers of the even orthogonal and symplectic subgroup of SL(2n, ) were computed in [Širola B., Normalizers and self-normalizing...
On classifie les orbites de sur l’immeuble de Bruhat-Tits de pour trois paires sphériques de groupes -adiques classiques.
Let X be a nice variety over a number field k. We characterise in pure “descent-type” terms some inequivalent obstruction sets refining the inclusion . In the first part, we apply ideas from the proof of by Skorobogatov and Demarche to new cases, by proving a comparison theorem for obstruction sets. In the second part, we show that if are such that , then . This allows us to conclude, among other things, that and .