Experimenting with Symplectic Hypergeometric Monodromy Groups

Hyperbolic Monodromy Groups for the Hypergeometric Equation and Cartan Involutions

We give a criterion which ensures that a group generated by Cartan involutions in the automorph group of a rational quadratic form of signature (n−1, 1) is “thin”, namely it is of infinite index in the latter. It is based on a graph defined on the integral Cartan root vectors, as well as Vinberg’s theory of hyperbolic reflection groups. The criterion is shown to be robust for showing that many ...

Monodromy of A-hypergeometric functions

Using Mellin-Barnes integrals we give a method to compute a relevant subgroup of the monodromy group of an A-hypergeometric system of differential equations. Presumably this group is the full monodromy group of the system

Experimenting with Infinite Groups, I

Theta functions on covers of symplectic groups

We study the automorphic theta representation $Theta_{2n}^{(r)}$ on the $r$-fold cover of the symplectic group $Sp_{2n}$‎. ‎This representation is obtained from the residues of Eisenstein series on this group‎. ‎If $r$ is odd‎, ‎$nle r

Big symplectic or orthogonal monodromy modulo `

Let k be a field not of characteristic two and Λ be a set consisting of almost all rational primes invertible in k. Suppose we have a varietyX/k and strictly compatible system {M` → X : ` ∈ Λ} of constructible F`-sheaves. If the system is orthogonally or symplectically self-dual, then the geometric monodromy group of M` is a subgroup of a corresponding isometry group Γ` over F`, and we say it h...