Related papers: Mixed Hodge modules and real groups

We study the deformations of twisted harmonic maps $f$ with respect to the representation $\rho$. After constructing a continuous "universal" twisted harmonic map, we give a construction of every first order deformation of $f$ in terms of…

We show that the category of mixed Hodge complexes admits a Cartan-Eilenberg structure, a notion introduced in [GNPR10] leading to a good calculation of the homotopy category in terms of (co)fibrant objects. This result provides a…

The relaxed highest weight representations introduced by Feigin et al. are a class of representations of the affine Kac-Moody algebra $\hat{\mathfrak{sl}_2}$, which do not have a highest (or lowest) weight. We formulate a generalization of…

Abstract. Let G be a complex reductive group and A be an Abelian variety of dimension d over $\mathbb{C}$. We determine the Poincar\'e polynomials and also the mixed Hodge polynomials of the moduli space $\mathcal{M}_{A}^{H}(G)$ of G-Higgs…

We study the Hodge numbers of Landau-Ginzburg models as defined by Katzarkov, Kontsevich and Pantev. First we show that these numbers can be computed using ordinary mixed Hodge theory, then we give a concrete recipe for computing these…

Let $U$ be a smooth connected complex algebraic variety, and let $f\colon U\to \mathbb C^*$ be an algebraic map. To the pair $(U,f)$ one can associate an infinite cyclic cover $U^f$, and (homology) Alexander modules are defined as the…

Let $H$ be a connected reductive subgroup of a complex connected reductive group $G$. Fix maximal tori and Borel subgroups of $H$ and $G$. Consider the pairs $(V,V')$ of irreducible representations of $H$ and $G$ such that $V$ is a…

Let $f:X\to Y$ be a morphism of complex manifolds. Suppose that $X$ is a K\"ahler manifold. Let $(\mathcal{T},\mathcal{S})$ be a regular polarized pure twistor $\mathcal{D}$-module of weight $w$ on $X$ whose support is proper over $Y$. We…

Let $G$ be a compact Lie group, $H$ a closed subgroup of maximal rank and $X$ a topological $G$-space. We obtain a variety of results concerning the structure of the $H$-equivariant K-ring $K_H^*(X)$ viewed as a module over the…

The first half of this paper is largely expository, wherein we present a systematic combinatorial approach to the theory of polynomial (semi)invariants and multilinear invariants of several vectors and covectors, for the classical groups.…

We prove that a variation of graded-polarizable mixed Hodge structure over a punctured disk with unipotent monodromy, has a limiting mixed Hodge structure at the puncture (i.e., it is admissible in the sense of [SZ]) which splits over $\R$,…

Given a family $X$ of complex varieties degenerating over a punctured disc, one is interested in computing related invariants called the motivic nearby fiber and the refined limit mixed Hodge numbers, both of which contain information about…

We show a few basic results about moduli spaces of semistable modules over Lie algebroids. The first result shows that such moduli spaces exist for relative projective morphisms of noetherian schemes, removing some earlier constraints. The…

Let $k$ be an algebraically closed field of odd characteristic $p$ and $X$ a proper smooth scheme over the Witt ring $W(k)$. To an object $(M,Fil^{\cdot},\nabla,\Phi)$ in the Faltings category $\mathcal{MF}^{\nabla}_{[0,n]}(X), n\leq p-2$,…

We present a combinatorial procedure (based on the W-graph of the Coxeter group) which shows that the characters of many intersection cohomology complexes on low rank complex flag varieties with coefficients in an arbitrary field are given…

Let k be an algebraically closed field of characteristic p>0 and let G be a symplectic or general linear group over k. We consider induced modules for G under the assumption that p is bigger than the greatest hook length in the partitions…

In this work we use Hodge theoretic methods to study homotopy types of complex projective manifolds with arbitrary fundamental groups. The main tool we use is the \textit{schematization functor} $X \mapsto (X\otimes \mathbb{C})^{sch}$,…

Let H and K be finite composition series of a group G. The intersections H_i\cap K_j of their members form a lattice CSL(H,\K) under set inclusion. Improving the Jordan-H\"older theorem, G. Gr\"atzer, J.B. Nation and the present authors…

The purpose of this work is to geometrize the notion of mixed Hodge structure. Therefore, we associate equivariant vector bundles on the projective plane to trifiltered vector spaces. Making this Rees construction with filtrations arising…

We give a $K$-theoretic and geometric interpretation for a generalized weighted Ehrhart theory of a full-dimensional lattice polytope $P$, depending on a given homogeneous polynomial function $\varphi$ on $P$, and with Laurent polynomial…