Global Pseudo-differential Operators on the Quantum Group $SU_q(2)$

Published 2 Apr 2018 in math.QA | (1804.00388v1)

Abstract: In this paper, following [1], we develop the theory of global pseudo-differential operators defined on the quantum group $SU_q(2)$, and provide some spectral results concerning these operators. We define a graduation for this algebra of pseudo-differential operators in terms of its natural Fourier decomposition and, using the infinite-dimensional representations introduced by Woronowicz [15], we also provide a $*$-representation of $SU_q(2)$ as bounded pseudo-differential operators acting on $L^{2(\mathbb{S}^1)$.}