Beurling-Fourier algebras of $ q $-deformations of compact semisimple Lie groups and complexification

TL;DR

This paper investigates Beurling-Fourier algebras for q-deformed compact semisimple Lie groups, revealing that their representation spaces are fully described by weighted Fourier algebras linked to specific central weights.

Contribution

It demonstrates that the irreducible representations of the Drinfeld doubles' function algebras are completely characterized by weighted Fourier algebras with central weights.

Findings

Representation spaces are exhausted by weighted Fourier algebras.

Irreducible representations are classified via central weights.

Provides new insights into q-deformations and their harmonic analysis.

Abstract

We study Beurling-Fourier algebras of $ q $-deformations of compact semisimple Lie groups. In particular, we show that the space of irreducible representations of the function algebras of their Drinfeld doubles is exhausted by the irreducible representations of weighted Fourier algebras associated to a certain family of central weights.