#### 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.

Done