A Khintchine inequality for central Fourier series on non-Kac compact quantum groups

The study of Khintchin inequalities has a long history in abstract harmonic analysis. While there is almost no possibility of non-trivial Khintchine inequality for central Fourier series on compact connected semisimple Lie groups, we demonstrate a strong contrast within the framework of compact quantum groups. Specifically, we establish a Khintchine inequality with operator coefficients for arbitrary central Fourier series in a large class of non-Kac compact quantum groups. The main examples include the Drinfeld-Jimbo q-deformations Gq, the free orthogonal quantum groups OF⁺, and the quantum automorphism group Gₐᵤₜ(B,ψ) with a δ-form ψ.