Let $\hat{\mathfrak{g}}$ be an untwisted affine Lie algebra or the twisted counterpart thereof (which excludes the affine Lie algebras of type ${\widehat{BC}}_n=A_{2n}^{(2)}$). We present an affine Pieri rule for a basis of periodic Macdonald spherical functions associated with $\hat{\mathfrak{g}}$. In type ${\hat{A}}_{n-1}=A_{n-1}^{(1)}$ the formula in question reproduces an affine Pieri 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 of genus zero $\widehat{\mathfrak{sl}}{(n)}_c$-Wess-Zumino-Witten conformal field theories.

中文翻译：

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周期麦克唐纳球函数和聚变环的仿射皮耶里规则

让 $\widehat{\mathfrak{G}}$ 是一个未扭曲的仿射李代数或其扭曲的对应物（不包括类型的仿射李代数 ${\widehat{乙C}}_n={\mathrm{一种}}_{2n}^{(2)}$）。我们提出了一个仿射皮耶里规则，用于与与$\widehat{\mathfrak{G}}$. 在类型${\widehat{\mathrm{一种}}}_{n-1}={\mathrm{一种}}_{n-1}^{(1)}$ 由于 Korff，该公式再现了圆柱 Hall-Littlewood 多项式的仿射 Pieri 规则，其在 $吨=0$ 专攻零属融合环中著名的皮耶里公式 $\widehat{\mathfrak{SL}}{(n)}_C$-Wess-Zumino-Witten 共形场理论。