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Let $\hat{\mathfrak{g}}$ be an untwisted affine Lie algebra or the twistedcounterpart thereof (which excludes the affine Lie algebras of type$\widehat{BC}_n=A^{(2)}_{2n}$). We present an affine Pieri rule for a basis ofperiodic Macdonald spherical functions associated with $\hat{\mathfrak{g}}$. Intype $\hat{A}_{n-1}=A^{(1)}_{n-1}$ the formula in question reproduces an affinePieri rule for cylindric Hall-Littlewood polynomials due to Korff, which at$t=0$ specializes in turn to a well-known Pieri formula in the fusion ring ofgenus zero $\widehat{\mathfrak{sl}}(n)_c$-Wess-Zumino-Witten conformal fieldtheories.

Affine Pieri rule for periodic Macdonald spherical functions and fusion rings