Related papers: Rigid local systems and alternating groups

Symmetries occur naturally in CSP or SAT problems and are not very difficult to discover, but using them to prune the search space tends to be very challenging. Indeed, this usually requires finding specific elements in a group of…

We investigate the possible structures imposed on a finite group by its possession of an automorphism sending a large fraction of the group elements to their cubes, the philosophy being that this should force the group to be, in some sense,…

We consider the class of countable groups possessing an action on a finite product of hyperbolic graphs where every infinite order element acts loxodromically. When the graphs are locally finite, we obtain strong structure theorems for the…

An orbit polytope is the convex hull of an orbit under a finite group $G \leq \operatorname{GL}(d,\mathbb{R})$. We develop a general theory of possible affine symmetry groups of orbit polytopes. For every group, we define an open and dense…

This survey is about old and new results about the modular representation theory of finite reductive groups with a strong emphasis on local methods. This includes subpairs, Brauer's Main Theorems, fusion, Rickard equivalences. In the…

We prove a fixed point theorem for the action of certain local monodromy groups on \'etale covers and use it to deduce lower bounds in essential dimension. In particular, we give more geometric proofs of many (but not all) of the results of…

We prove a general homological stability theorem for certain families of groups equipped with product maps, followed by two theorems of a new kind that give information about the last two homology groups outside the stable range. (These…

We provide algorithms to compute a complete irredundant set of extremely strong Shoda pairs of a finite group $G$ and the set of the primitive central idempotents of the rational group algebra $\mathbb{Q}[G]$ realized by them. These…

Consider a smooth connected algebraic group $G$ acting on a normal projective variety $X$ with an open dense orbit. We show that Aut($X$) is a linear algebraic group if so is $G$; for an arbitrary $G$, the group of components of Aut($X$) is…

Let $\{\rho_{\ell}:\mathrm{Gal}_K\to\mathrm{GL}_n(\mathbb{Q}_{\ell})\}_{\ell}$ be a semisimple compatible system of $\ell$-adic representations of a number field $K$ that is arising from geometry. Let…

We consider all irreducible rank-4 hypergeometric local systems defined over $\mathbb{Q}$ that support a rational one-dimensional variation of Hodge structures of weight 3 and Hodge vector $(1,1,1,1)$. Up to a natural equivalence there are…

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r)…

We prove structure theorems for the moduli stack of elliptic curves equipped with $G$-structures, where $G$ is a finite 2-generated metabelian group. In particular, we show that if $G$ has exponent $e$, then there is a subgroup $H\le…

For a prime number $p$, we show that if two certain canonical finite quotients of a finitely generated Bloch-Kato pro-$p$ group $G$ coincide, then $G$ has a very simple structure, i.e., $G$ is a $p$-adic analytic pro-$p$ group. This result…

A computation shows that there are 77 (up to scalar shifts) possible pairs of integer coefficient polynomials of degree five, having roots of unity as their roots, and satisfying the conditions of Beukers and Heckman [1], so that the…

A new family of local-global conjectures in the representation theory of finite groups has recently been proposed by Moret\'o. We show that one of the strongest of these conjectures, the strong subnormalizer conjecture, holds for…

In [Akbari and Moghaddamfar, Recognizing by order and degree pattern of some projective special linear groups, {\it Internat. J. Algebra Comput.}, 2012] the authors possed the following problem: \\ {\bf Problem.} {\it Is there a simple…

We prove the finiteness of Selmer groups attached to lifts of certain 2-dimensional mod p representations of the absolute Galois group of Q. The mod p representation can be either even or odd. The lifts considered are the ones that were…

We exhibit an infinite family of discrete subgroups of ${Sp}_4(\mathbb R)$ which have a number of remarkable properties. Our results are established by showing that each group plays ping-pong on an appropriate set of cones. The groups arise…

The subject matter of this paper is the geometry of the affine group over the integers, $\mathsf{GL}(n,\mathbb{Z})\ltimes \mathbb{Z}^n$. Turing-computable complete $\mathsf{GL}(n,\mathbb{Z})\ltimes \mathbb{Z}^n$-orbit invariants are…