Author’s introduction: A basic result of Harish-Chandra says that the center of the enveloping algebra \(U(\mathfrak g)\) of a complex semisimple Lie algebra \(\mathfrak g\) is isomorphic to the representation ring of the category of finite-dimensional representations of \(\mathfrak g\). Indeed, both rings are polynomial rings in rank \(\mathfrak g\) generators, but there is no natural isomorphism between them. The situation improves when one passes from Lie algebras to quantum groups; here Drinfeld and Reshetikhin have constructed a natural isomorphism from the representation ring to the center of \(U_q(\mathfrak g)\) which can be written down explicitly [V. G. Drinfeld, in: Proc. Int. Congress Math., Berkeley/Calif. 1986, Vol. 1, 798-820, (1987; Zbl 0667.16003); N. Yu. Reshetikhin, Leningr. Math. J. 1, No. 2, 491-513 (1990); translation from Algebra Anal. 1, No. 2, 169-188 (1989; Zbl 0715.17016)]. The construction of the isomorphism extends to the case where \(\mathfrak g\) is a symmetrizable Kac-Moody algebra. Here the author sketches this extension briefly and then makes it explicit in the special case where \(\mathfrak g\) is affine (untwisted) \(\mathfrak s\mathfrak l_n\). The central elements in the quantum group turn out to be affine analogues of Macdonald’s difference operators preserving the space of symmetric theta functions. They thus admit a unique common eigenbasis (up to scalar multiples) in this space, which coincides with the basis of affine Macdonald polynomials defined in [P. I. Etingof and A. A. Kirillov jun. Duke Math. J. 78, No. 2, 229-256 (1995; Zbl 0873.33011)].