Non-arithmetic monodromy of higher hypergeometric functions

TL;DR

This paper demonstrates that all known non-arithmetic lattices in PU(2,1) can be realized as monodromy groups of higher hypergeometric functions, linking geometric structures with special functions.

Contribution

It establishes a connection between non-arithmetic lattices in PU(2,1) and monodromy groups of higher hypergeometric functions, a novel unification in the field.

Findings

All known non-arithmetic lattices in PU(2,1) are monodromy groups of higher hypergeometric functions.

Provides a new perspective on the structure of non-arithmetic lattices.

Links geometric group theory with special functions through monodromy representations.

Abstract

We show that all the currently known non-arithmetic lattices in ${\rm PU}(2,1)$ are monodromy groups of higher hypergeometric functions.