Related papers: Local systems and Suzuki groups

Deligne constructed a remarkable local system on $\bP^1-\{0,\infty\}$ attached to a family of Kloosterman sums. Katz calculated its monodromy and asked whether there are Kloosterman sheaves for general reductive groups and which automorphic…

A p-local finite group is an algebraic structure with a classifying space which has many of the properties of p-completed classifying spaces of finite groups. In this paper, we construct a family of 2-local finite groups, which are exotic…

For the universal family of cyclic covers of projective spaces branched along hyperplane arrangements in general position, we consider its monodromy group acting on an eigen linear subspace of the middle cohomology of the fiber. We prove…

We show how the theory of affine geometries over the ring ${\mathbb Z}/\langle q - 1\rangle$ can be used to understand the properties of toric and generalized toric codes over ${\mathbb F}_q$. The minimum distance of these codes is strongly…

We give the monodromy representations of local systems of twisted homology groups associated with Lauricella's system $F_D(a,b,c)$ of hypergeometric differential equations under mild conditions on parameters. Our representation is effective…

For an algebraically closed field K, let G be a finite abelian group of K-linear automorphisms of a finite-dimensional path algebra KQ of a quiver Q. Under certain assumptions on the action of G, we show the existence of a certain kind of…

Strong external difference family (SEDF) and its generalizations GSEDF, BGSEDF in a finite abelian group $G$ are combinatorial designs raised by Paterson and Stinson [7] in 2016 and have applications in communication theory to construct…

Gauss hypergeometric functions with a dihedral monodromy group can be expressed as elementary functions, since their hypergeometric equations can be transformed to Fuchsian equations with cyclic monodromy groups by a quadratic change of the…

We study gauge symmetry in F-theory in light of global aspects. For this, we consider not only a simple (local) group, but also a semi-simple group with Abelian factors. Once we specify the complete gauge group by decomposing the…

We study Seiberg-Witten (SW) geometries for rank-two theories, encompassing 4D field theories as well as 5D and 6D Kaluza-Klein (KK) theories. The singular model for each SW geometry is derived from a one-parameter family of algebraic…

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…

We show that the affine quantum group $U_q(\hat{sl_2})$ is isomorphic to a bicrossproduct central extension $C Z{}_\chi\cross U_q(Lsl_2)$ of the quantum loop group $U_q(Lsl_2)$ by a quantum cocycle $\chi$, which we construct. We prove the…

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…

A question of Griffiths-Schmid asks when the monodromy group of an algebraic family of complex varieties is arithmetic. We resolve this in the affirmative for the class of algebraic surfaces known as Atiyah-Kodaira manifolds, which have…

We present an approach to construct a class of generalized Frobenius manifold structures on the orbit spaces of affine Weyl groups, and prove that their monodromy groups are parabolic subgroups of the associated affine Weyl groups.

Explicit generators are found for the group $G_2$ of automorphisms of the algebra $\mS_2$ of one-sided inverses of a polynomial algebra in two variables over a field of characteristic zero. Moreover, it is proved that $$ G_2\simeq…

Among the infinite classes of finite simple groups, the most exotic classes are probably the Suzuki groups and the Ree groups. They are "twisted versions" of groups of Lie type, but they cannot be directly obtained as groups of rational…

Let $K$ be a 2-dimensional global field of characteristic $\neq 2$, and let $V$ be a divisorial set of places of $K$. We show that for a given $n \geqslant 5$, the set of $K$-isomorphism classes of spinor groups $G = \mathrm{Spin}_n(q)$ of…

We study smooth cubic fourfolds admitting an automorphism of order $7$. It is known that the possible symplectic automorphism groups of such cubic fourfolds are precisely $F_{21}$, $\mathrm{PSL}(2,\mathbb{F}_7)$, and $A_7$. In this paper,…

A certain "condition (S)" on reductive algebraic groups was introduced in [GT2], in which a slightly stronger condition (S+) was shown to have very strong consequences. We show that a wide class of Kloosterman and hypergeometric sheaves…