Related papers: Singular supports for character sheaves on a group…

We show that stationary characters on irreducible lattices $\Gamma < G$ of higher-rank connected semisimple Lie groups are conjugation invariant, that is, they are genuine characters. This result has several applications in representation…

The theory of character sheaves on a reductive group is extended to a class of varieties which includes the strata of the De Concini-Procesi completion of an adjoint group.

We give a systematic construction of semiorthogonal decompositions of derived categories of coherent sheaves on quasi-smooth derived algebraic stacks over $\mathbb{C}$, where the summands are subcategories defined by weight conditions, and…

The branched deformations of immersed compact special Lagrangian submanifolds are studied in this paper. If there exists a nondegenerate $\mathbb{Z}_2$ harmonic 1-form over a special Lagrangian submanifold $L$, we construct a family of…

Assume $G$ is a connected reductive algebraic group defined over $\bar{\mathbb{F}_p}$ such that $p$ is good prime for $G$. Furthermore we assume that $Z(G)$ is connected and $G/Z(G)$ is simple of classical type. Let $F$ be a Frobenius…

We suggest a general framework for compactifing quasi-projective Lagrangian fibrations of geometric origin by holomorphic symplectic varieties. This framework includes a compactification criterion, which we then apply to various fibrations…

Recently, a strong exponential character bound has been established in [3] for all elements $g \in \mathbf{G}^F$ of a finite reductive group $\mathbf{G}^F$ which satisfy the condition that the centraliser $C_{\mathbf{G}}(g)$ is contained in…

Let $G$ be a complex linear algebraic group which is simple of adjoint type. Let $\overline G$ be the wonderful compactification of $G$. We prove that the tangent bundle of $\overline G$ is stable with respect to every polarization on…

Let Y be a compact reduced subspace of a complex manifold X, and let F be a subsheaf of the tangent bundle T_X which is closed under the Lie bracket. This paper discusses criteria to guarantee that infinitesimal deformations of the…

We study Lagrangian subalgebras of a semisimple Lie algebra with respect to the imaginary part of the Killing form. We show that the variety $\Lagr$ of Lagrangian subalgebras carries a natural Poisson structure $\Pi$. We determine the…

We prove a conjecture of Lusztig on a microlocal characterization of his perverse sheaves. For any finite quiver without loops, an equivariant simple perverse sheaf on the variety of quiver representations is a Lusztig's perverse sheaf if…

In this note, we introduce the notion of a singular principal G-bundle, associated to a reductive algebraic group G over the complex numbers by means of a faithful representation $\varrho^\p\colon G\lra \SL(V)$. This concept is meant to…

Let $X \subset \mathbb{C}^n$ be an algebraic variety, and let $\Lambda \subset \mathbb{C}^n$ be a discrete subgroup whose real and complex spans agree. We describe the topological closure of the image of $X$ in $\mathbb{C}^n / \Lambda$,…

Let $\mathcal{X}_{\Gamma}G:=\mathrm{Hom}(\Gamma,G)/\!/G$ be the $G$-character variety of $\Gamma$, where $G$ is a complex reductive group and $\Gamma$ a finitely presented group. We introduce new techniques for computing Hodge-Deligne and…

Let Y be a weighted homogeneous (singular) subvariety of C^n. The main objective of this paper is to present a class of explicit integral formulae for solving the d-bar-equation $\omega=\dbar\lambda$ on the regular part of Y, where $\omega$…

We explore the cohomological structure for the (possibly singular) moduli of $\mathrm{SL}_n$-Higgs bundles for arbitrary degree on a genus g curve with respect to an effective divisor of degree >2g-2. We prove a support theorem for the…

We define the notion of special Lagrangian curvature, showing how it may be interpreted as an alternative higher dimensional generalisation of two dimensional Gaussian curvature. We obtain first a local rigidity result for this curvature…

In the first part of this paper we consider compact algebraic manifolds M^2n with an algebraic (n-1)-Torus action. We show that there is a T-invariant meromorphic section $\sigma$ of the canonical bundle of M. Any such $\sigma$ defines a…

We introduce support varieties for rational representations of a linear algebraic group $G$ of exponential type over an algebraically closed field $k$ of characteristic $p > 0$. These varieties are closed subspaces of the space $V(G)$ of…

Let $G$ be a simply connected Lie group with Lie algebra $\mathfrak{g}$ and denote by $\mathrm{C}_{\bullet}(G)$ the DG Hopf algebra of smooth singular chains on $G$. In a companion paper it was shown that the category of sufficiently smooth…