Alladi Ramakrishnan Hall

Monodromy groups of hypergeometric functions

T N Venkataramana

TIFR, Mumbai

The Gauss hypergeometric function (and the Clausen-Thomae
hypergeometric function) satisfies a second order linear differential
euqation (a higher order equation) whose coefficients are analytic on the
projective line minus three points; at these points the equations have
regular singularities. We thus get a monodromy representation on the
space of solutions of this equation whose image is the hypergeometric
group.

In this talk we consider hypergeometric groups of symplectic and
orthogonal type and show that in many cases, the monodromy groups are
arithmetic groups, and that in many cases they are not.