Tensor Products and Discriminants of Unital Quadratic Forms over Commutative Rings.
The Brauer category and invariant theory
A category of Brauer diagrams, analogous to Turaev’s tangle category, is introduced, a presentation of the category is given, and full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O or the symplectic group Sp over any field of characteristic zero. The first and second fundamental theorems of invariant theory for these classical groups are generalised to the category theoretic setting. The major outcome is that we obtain presentations...
The centralizer of a classical group and Bruhat-Tits buildings
Let be a unitary group defined over a non-Archimedean local field of odd residue characteristic and let be the centralizer of a semisimple rational Lie algebra element of We prove that the Bruhat-Tits building of can be affinely and -equivariantly embedded in the Bruhat-Tits building of so that the Moy-Prasad filtrations are preserved. The latter property forces uniqueness in the following way. Let and be maps from to which preserve the Moy–Prasad filtrations. We prove that...
The First Cohomology Group of a Line Bundle on G/B.
The Invariants of Unipotent Radicals of Parabolic Subgroups.
The normality of closures of orbits in a Lie algebra.
The split building of a reductive group.
The Waring loci of ternary quartics.
Torsion in cohomology of compact Lie groups and Chow rings of reductive algebraic groups.
Transience of algebraic varieties in linear groups - applications to generic Zariski density
We study the transience of algebraic varieties in linear groups. In particular, we show that a “non elementary” random walk in escapes exponentially fast from every proper algebraic subvariety. We also treat the case where the random walk takes place in the real points of a semisimple split algebraic group and show such a result for a wide family of random walks.As an application, we prove that generic subgroups (in some sense) of linear groups are Zariski dense.
Transvectants des formes binaires et représentations des groupes binaires polyhedraux