Related papers: On Parabolic Subgroups of Symplectic Reflection Gr…

We define strict C(n) small-cancellation complexes, intermediate to C(n) and C(n+1), and we prove groups acting properly cocompactly on a simply-connected strict C(6) complex are hyperbolic relative to a collection of maximal virtually free…

We obtain a number of finiteness results for groups acting on Gromov-hyperbolic spaces. In particular we show that a torsion-free locally quasiconvex hyperbolic group has only finitely many conjugacy classes of $n$-generated one-ended…

We investigate positive-dimensional closed reductive subgroups of almost simple algebraic groups containing a regular unipotent element. Our main result states that such subgroups do not lie inside proper parabolic subgroups unless possibly…

We apply Zhang's almost K\"ahler Nakai-Moishezon theorem and Li-Zhang's comparison of $J$-symplectic cones to establish a stability result for the symplectomorphism group of a rational $4$-manifold $M$ with Euler number up to $12$. As a…

We construct analogues of FI-modules where the role of the symmetric group is played by the general linear groups and the symplectic groups over finite rings and prove basic structural properties such as Noetherianity. Applications include…

In this paper we shall prove that the singular locus of a symplectic singularity has no codimension 3 irreducible components. As a corollary, a symplectic singularity is terminal if and only if its singular locus has codimension $\geq 4$.…

We investigate the "two-parameter" quantum symmetry groups that we previously constructed with Skalski, with the conclusion that some of these quantum groups, namely those without singletons, are "super-easy" in a suitable sense, that we…

In this article we study rational Cherednik algebras at $t = 1$ in positive characteristic. We study a finite dimensional quotient of the rational Cherednik algebra called the restricted rational Cherednik algebra. When the corresponding…

We prove a slope 1 stability range for the homology of the symplectic, orthogonal and unitary groups with respect to the hyperbolic form, over any fields other than $F_2$, improving the known range by a factor 2 in the case of finite…

There is a well-known correspondence between the symplectic variety of representations of the fundamental group of a punctured Riemann surface into a compact Lie group G, with fixed conjugacy classes at the punctures, and a complex variety…

A remarkable result of Gersten states that the class of hyperbolic groups of cohomological dimension $2$ is closed under taking finitely presented (or more generally $FP_2$) subgroups. We prove the analogous result for relatively hyperbolic…

This paper is a complement to the work of the second author on modular quotient singularities in odd characteristic (see arXiv:1210.8006). Here we prove that if $V$ is a three-dimensional vector space over a field of characteristic $2$ and…

We improve the homology stability range for the 3rd integral homology of symplectic groups over commutative local rings with infinite residue field. As an application, we show that for local commutative rings containing an infinite field of…

We improve, by a factor of 2, known homology stability ranges for the integral homology of symplectic groups over commutative local rings with infinite residue field and show that the obstruction to further stability is bounded below by…

We define parabolic quasi-Coxeter elements in well generated complex reflection groups. We characterize them in multiple natural ways, and we study two combinatorial objects associated with them: the collections $\operatorname{Red}_W(g)$ of…

In this paper, we study the solvmanifolds constructed from any parabolic subalgebras of any semisimple Lie algebras. These solvmanifolds are naturally homogeneous submanifolds of symmetric spaces of noncompact type. We show that the Ricci…

For any rational prime $p$, we define a certain $p$-stabilization of holomorphic Siegel Eisenstein series for the symplectic group $\text{Sp}(2n)_{/\mathbb{Q}}$ of an arbitrary genus $n \ge 1$. In addition, we derive an explicit formula for…

We provide a general construction of convex cocompact hyperbolic reflection groups with three-dimensional limit sets. More precisely, our construction takes as input an arbitrary simplicial complex L of dimension 3 on n vertices, and…

We build quasi--isometry invariants of relatively hyperbolic groups which detect the hyperbolic parts of the group; these are variations of the stable dimension constructions previously introduced by the authors. We prove that, given any…

We show that in characteristic 2, the Steinberg representation of the symplectic group Sp(2n,q), q a power of an odd prime p, has two irreducible constituents lying just above the socle that are isomorphic to the two Weil modules of degree…