Arithmeticity of certain Symplectic Monodromy Groups
Sandip Singh (Mainz)
What 


When 
Nov 07, 2013 from 03:15 pm to 04:15 pm 
Where  Mainz, 05432 (Hilbertraum) 
Add event to calendar 
vCal iCal 
Abstract: Monodromy groups of hypergeometric differential
equations are defined as image of the fundamental group $G$ of Riemann sphere
minus three points namely 0, 1 and the point at infinity, under some certain
representation of $G$ inside the general linear group $GL_n$. By a theorem of
Levelt (1961), the monodromy groups are (up to conjugation in $GL_n$) the
subgroups of $GL_n$ generated by the companion matrices of two degree $n$
polynomials $f$ and $g$ with complex coefficients and having no common roots.
If we start with $f$, $g$ two integer coefficient polynomials of degree $n$ (an
even integer) which satisfy some "conditions" with $f(0)=g(0)=1$,
then the associated monodromy group preserves a nondegenerate integral
symplectic form, that is, the monodromy group is contained in the integral
symplectic group of the associated symplectic form.
In this talk, we will describe a sufficient condition on a pair of the
polynomials that the associated monodromy group is an arithmetic subgroup (a
subgroup of finite index) of the integral symplectic group.