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

2018/04/02 by Torijano, Carlos Andres Rodriguez
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1804.00388

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 L²(\mathbbS¹).

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