On the arithmeticity of hypergeometric monodromy groups

The monodromy groups of hypergeometric differential equations are characterised as the subgroups of GL_n generated by the companion matrices of two monic co-prime polynomials of degree n, and the Zariski closure of these groups inside GL_n is either symplectic or orthogonal group.

In this talk, we will describe a sufficient condition on a pair of the polynomials that the associated monodromy group is an arithmetic subgroup of the symplectic group, and show some examples of arithmetic orthogonal monodromy groups.