Related papers: Borel class and Cartan involution

We compute the E-polynomial of the character variety of representations of a rank r free group in SL(3, C). Expanding upon existing techniques, we stratify the space of representations and compute the E-polynomial of each geometrically…

We prove that the mapping class group of a closed connected orientable surface of genus $g$ is generated by three involutions for $g\geq 6$.

We prove some formulas relating the inverse of a Cartan matrix with algebraic and geometric invariants of finite group representations.

We prove a long-standing conjecture of Geck which predicts that cuspidal unipotent characters remain irreducible after $\ell$-reduction. To this end, we construct a progenerator for the category of representations of a finite reductive…

We classify representations of a class of Deligne-Mostow lattices into PGL(3;C). In particular, we show local rigidity for the representations (of Deligne-Mostow lattices with 3-fold symmetry and of type one) where the generators we chose…

We prove a reduced version of the Chevalley restriction conjecture on the commuting scheme posed by T.H. Chen and B.C. Ng\^o, extending the results of Hunziker for classical groups. In particular, we prove that for any connected reductive…

In this article we introduce order preserving representations of fundamental groups of surfaces into Lie groups with bi-invariant orders. By relating order preserving representations to weakly maximal representations, introduced in…

We prove that braid group representations associated to braided fusion categories and mapping class group representations associated to modular fusion categories are always semisimple. The proof relies on the theory of extensions in…

In this paper, for n a positve integer, we compute the number of n degree representations for a dihedral group G of order 2m, m \geq 3 and the dimensions of the corresponding spaces of G invariant bilinear forms over a complex field C. We…

We prove a categorical version of the Torelli theorem for cubic threefolds. More precisely, we show that the non-trivial part of a semi-orthogonal decomposition of the derived category of a cubic threefold characterizes its isomorphism…

Recently, John Franks and Michael Handel proved that, for $g\geq 3$ and $n\leq 2g-4$, every homomorphism from the mapping class group of an orientable surface of genus $g$ to $\GL (n,\C)$ is trivial. We extend this result to $n\leq 2g-1$,…

We classify involutions acting on spherical 3-manifolds up to conjugacy. Our geometric approach provides insights into numerous topological properties of these involutions.

We consider a group SO(2n+1) over a p-adic field, and tempered irreducible representations of this group, of unipotent reduction. We use the construction due to Lusztig of these representations. In an old paper with Moeglin, we have defined…

We study the so-called sign involutions on twisted forms of abelian varieties, and show that such a sign involution exists if and only if the class in the Weil--Ch\^{a}telet group is annihilated by two. If these equivalent conditions hold,…

We consider 3-manifolds admitting the action of an involution such that its space of orbits is homeomorphic to $S^3.$ Such involutions are called hyperelliptic as the manifolds admitting such an action. We consider finite groups acting on…

We define a class of morphisms between \'etale groupoids and show that there is a functor from the category with these morphisms to the category of $C^*$-algebras. We show that all homomorphisms between Cartan pairs of $C^*$-algebras that…

We prove two results on convex subsets of Euclidean spaces invariant under an orthogonal group action. First, we show that invariant spectrahedra admit an equivariant spectrahedral description, i.e., can be described by an equivariant…

It is shown, that the mapping class group of a surface of the genus g > 1 admits a faithful representation into the matrix group GL (6g-6, Z). The proof is based on a categorical correspondence between the Riemann surfaces and the so-called…

Let $ M$ be a cusped hyperbolic $ 3$-manifold, e.g. a knot complement. Thurston showed that the space of deformations of its fundamental group in $ \mathrm {PGL}(2,\mathbf {C})$ (up to conjugation) is of complex dimension the number $ \nu $…

We introduce a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. We prove for instance that if the fundamental group of a compact aspherical manifold M has FDC, and if N is…