Invariant triple functionals over $U_q\frak{sl}_2$

TL;DR

This paper introduces a q-deformation of certain representations of GL_2(R) and proves the uniqueness of an invariant triple functional on these representations, extending classical results to a quantum setting.

Contribution

It defines a new q-deformation of Jacquet-Langlands principal series representations and establishes the uniqueness of an invariant triple functional in this quantum context.

Findings

Established a q-deformation of principal series representations

Proved the uniqueness of the invariant triple functional in the deformed setting

Extended classical representation theory results to quantum groups

Abstract

We define a $q$-deformation of Jacquet-Langlands principal series representations of $GL_2(R)$ and prove the uniqueness of an invariant triple functional on them using the method of H.Y.Loke.