Fuchsian groups of the second kind and representations carried by the limit set

TL;DR

This paper computes the cohomology of second kind Fuchsian groups using hyperfunction vectors from principal series representations, focusing on the limit set, advancing understanding of their geometric and algebraic properties.

Contribution

It introduces a novel method for calculating cohomology of Fuchsian groups of the second kind via hyperfunction vectors supported on the limit set.

Findings

Cohomology groups are explicitly computed for these Fuchsian groups.

The approach links geometric limit sets with algebraic representation theory.

Results enhance understanding of the structure of Fuchsian groups and their representations.

Abstract

We compute the cohomology of a Fuchsian group of the second kind with coefficients in the hyperfunction vectors of the principal series representations of $SL(2,R)$ supported on the limit set.