For the quantum symplectic group SP q (2n), we describe the C * -algebra of continuous functions on the quotient space SP q (2n)/SP q (2n − 2) as a universal C * -algebra given by a finite set of generators and relations. The proof involves a careful analysis of the relations, and use of the branching rules for representations of the symplectic group due to Zhelobenko. We then exhibit a set of generators of the K-groups of this C
In this article, we obtain a complete list of inequivalent irreducible representations of the compact quantum group U q (2) for non-zero complex deformation parameters q, which are not roots of unity. The matrix coefficients of these representations are described in terms of the little q-Jacobi polynomials. The Haar state is shown to be faithful and an orthonormal basis of L 2 (U q (2)) is obtained. Thus, we have an explicit description of the Peter-Weyl decomposition of U q (2). As an application, we discuss the Fourier transform and establish the Plancherel formula. We also describe the decomposition of the tensor product of two irreducible representations into irreducible components. Finally, we classify the compact quantum groups U q (2).
In this paper, we associate a growth graph and a length operator to a quotient space of a semisimple compact Lie group. Under certain assumptions, we show that the spectral dimension of a homogeneous space is greater than or equal to summability of the length operator. Using this, we compute spectral dimensions of spheres.
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