Related papers: A remark on cuspidal local systems

We study the finite-dimensional continuous complex representations of $\mathrm{SL}_2$ over the ring of integers of non-Archimedean local fields of even residual characteristic. We prove that for characteristic two, the abscissa of…

We show that for any integer n and any field k of characteristic different from 2 there are at most finitely many isomorphism classes of quadratic morphisms from the projective line over k to itself with a finite postcritical orbit of size…

We study the generalized doubling method for pairs of representations of $G\times GL_k$ where $G$ is a symplectic group, split special orthogonal group or split general spin group. We analyze the poles of the local integrals, and prove that…

We show that every amenable group with a locally invariant partial order has a left-invariant total order (and is therefore locally indicable). We also show that if a group G admits a left-invariant total order, and H is a locally nilpotent…

In earlier work of the author rigid irregular connections with differential Galois group $G_2$ and whose slopes have numerator $1$ were classified and new rigid connections were constructed. The same construction can be carried out for…

In the introduction of this paper we discuss a possible approach to the unitarizability problem for classical p-adic groups. In this paper we give some very limited support that such approach is not without chance. In a forthcoming paper we…

We show how the classification of simple singularities of functions can be reduced directly, not using the normal forms, to the classification of irreducible Weyl groups. We also prove that the class of a singularity in its local algebra…

We determine precisely which irreducible hypergeometric sheaves have an extraspecial normalizer in characteristic 2 as their geometric monodromy groups. This resolves the last open case of the determination of local monodromy at 0 of…

Let $X/\mathbb{F}_{q}$ be a smooth geometrically connected variety. Inspired by work of Corlette-Simpson over $\mathbb{C}$, we formulate a conjecture that absolutely irreducible rank 2 local systems with infinite monodromy on $X$ come from…

Let $k$ be a nonperfect separably closed field. Let $G$ be a connected reductive algebraic group defined over $k$. We study rationality problems for Serre's notion of complete reducibility of subgroups of $G$. In particular, we present a…

We prove that if $A$ is a computable Hopfian finitely presented structure, then $A$ has a computable $d$-$\Sigma_2$ Scott sentence if and only if the weak Whitehead problem for $A$ is decidable. We use this to infer that every hyperbolic…

Let G be a possibly disconnected reductive group over a finite field with Frobenius map F. The main result of this paper is that the characteristic functions af "admissible complexes" A on G such that F^*A is isomorphic to A form a basis of…

In this paper we describe all group gradings by a finite abelian group $\Gamma$ of a simple Lie algebra of type $G_2$ over an algebraically closed field $F$ of characteristic 0.

It is known that multiplicity one property holds for SL(2), while the strong multiplicity one property fails. However, in this paper, we show that if we require further that a pair of cuspidal representations $\pi$ and $\pi'$ of SL(2) have…

We show that the following problems are decidable in a rank 2 free group F_2: does a given finitely generated subgroup H contain primitive elements? and does H meet the orbit of a given word u under the action of G, the group of…

In this article, we are concerned with the Langlands functoriality conjecture. Cogdell, Kim, Piatetski-Shapiro and Shahidi proved functioriality conjecture in the case of a globally generic cuspidal automorphic representation for the split…

In this paper, we demonstrate the non-existence of a computational algorithm capable of determining whether the second homotopy group of any compact constructive topological space is trivial. This finding shows the inherent limitations of…

We construct here the first known examples of non-split sharply 2-transitive groups of bounded exponent in odd positive characteristic for every large enough prime $p \equiv 3 \pmod{4}$. In fact, we show that there are countably many…

We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such…

We characterize the toric face rings that are normal (respectively seminormal). Extending results about local cohomology of Brun, Bruns, Ichim, Li and R\"omer of seminormal monoid rings and Stanley toric face rings, we prove the vanishing…