Complex hyperbolic representations of SL2(R)

TL;DR

This paper introduces a new two-parameter family of representations for SL2(R) by developing a complete invariant and binary combination for its irreducible representations, advancing the understanding of their structure.

Contribution

It presents a novel two-parameter family of representations for SL2(R) based on a complete invariant and binary combination, expanding the classification framework.

Findings

Defined a complete invariant for irreducible representations

Introduced a binary combination for these representations

Established a new family of representations for SL2(R)

Abstract

A complete invariant and a binary combination for irreducible representations of SL2(R) are introduced. With this, a new two-parameter family of representations is defined.