相关论文: Twisted geometric Satake equivalence via gerbes on…

Using the equivalence between Scherk-Schwarz reductions and twisted tori compactifications, we discuss the effective theories obtained by this procedure from M-theory and N =4 type II orientifold constructions with Neveu-Schwarz and…

Let G be a reductive algebraic group over a field k. When k=C, R.K.Brylinski constructed a filtration of weight spaces of a G module, using the action of a principal nilpotent element of the Lie algebra, and proved that this filtration…

We prove that twisted $\ell^2$-Betti numbers of locally indicable groups are equal to the usual $\ell^2$-Betti numbers rescaled by the dimension of the twisting representation; this answers a question of L\"uck for this class of groups. It…

We associate to an arbitrary positive root $\alpha$ of a complex semisimple finite-dimensional Lie algebra $\mfrak{g}$ a twisting endofunctor $T_\alpha$ of the category of $\mfrak{g}$-modules. We apply this functor to generalized Verma…

We generalize the higher Riemann-Hilbert correspondence in the presence of scalar curvature for a (possibly non-compact) smooth manifold $M$. We show that the dg-category of curved $\infty$-local systems, the dg-category of graded vector…

We develop a "Soergel theory" for Bruhat-constructible perverse sheaves on the flag variety $G/B$ of a complex reductive group $G$, with coefficients in an arbitrary field $\Bbbk$. Namely, we describe the endomorphisms of the projective…

Lyubashenko's construction associates representations of mapping class groups Map_{g,n} of Riemann surfaces of any genus g with any number n of holes to a factorizable ribbon category. We consider this construction as applied to the…

We prove that for any k greater or equal to 2, given a smooth compact k-dimensional manifold and a multiplicative k-1-gerbe on a Lie group, together with an integrable connection, there is a line bundle on the corresponding…

We show that the distributions occurring in the geometric and spectral side of the twisted Arthur-Selberg trace formula extend to non-compactly supported test functions. The geometric assertion is modulo a hypothesis on root systems proven…

For the Grothendieck group of a split simple linear algebraic group, the twisted gamma-filtration provides a useful tool for constructing torsion elements in gamma-rings of twisted flag varieties. In this paper, we construct a non-trivial…

For a normal projective variety $X$, the $\bf Q$-factoriality defect $\sigma(X)$ is defined to be the rank of the quotient of the group of Weil divisors by the subgroup of Cartier ones. We prove a slight improvement of a topological formula…

Given a simply-connected simple algebraic group $G$, we determine the tangent space of any Finkelberg-Mirkovi\'c Schubert scheme at the base point of the affine Grassmannian of $G$. As a consequence, we exhibit non-reduced…

This article proves, in the case of split groups over arbitrary fields, that all fibers of convolution morphisms attached to parahoric affine flag varieties are paved by products of affine lines and affine lines minus a point. This applies…

In a 1983 paper the author has established a (decategorified) Satake equivalence for affine Hecke algebras. In this paper we give new proofs for some results of that paper, one based on the theory of J-rings and one based on the known…

We make explicit Serre's generalization of the Sato-Tate conjecture for motives, by expressing the construction in terms of fiber functors from the motivic category of absolute Hodge cycles into a suitable category of Hodge structures of…

We study the fate of discrete gauge groups and discrete charges of gravitational theories under twisted circle compactification. We then apply our results to six-dimensional F-theory vacua with discrete gauge symmetries and relate them to…

We generalize the concept of Sato Grassmannians of locally linearly compact topological vector spaces (Tate spaces) to the category limA of the "locally compact objects" of an exact category A, and study some of their properties. This…

In this article, we develop the theory of stratified perverse Nori motives to prove a refinement of the geometric Satake equivalence of Mirkovi\'c-Vilonen, for which we call the Nori motivic Satake equivalence, in contrast to the "Tate…

We prove an equivalence between filtrations of primitive bialgebras and filtrations of factorizable perverse sheaves, generalizing the results obtained by Kapranov-Schechtman. Under this equivalence, we find that the word length filtration…

For each integral dominant weight $\lambda$, we construct a twisted global section functor $\Gamma^{\lambda}$ from the category of critical twisted $D$-modules on affine Grassmannian to the category of $\lambda$-regular modules of affine…