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arXiv · 2305.01931

Affine Pieri rule for periodic Macdonald spherical functions and fusion rings

Jan Felipe van Diejen·Erdal Emsiz·Ignacio N. Zurrián
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Abstract

Let $\hat{\mathfrak{g}}$ be an untwisted affine Lie algebra or the twisted counterpart thereof (which excludes the affine Lie algebras of type $\widehat{BC}_n=A^{(2)}_{2n}$). We present an affine Pieri rule for a basis of periodic Macdonald spherical functions associated with $\hat{\mathfrak{g}}$. In type $\hat{A}_{n-1}=A^{(1)}_{n-1}$ 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.

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BibTeXRIS

Jan Felipe van Diejen, Erdal Emsiz, Ignacio N. Zurrián. 2023-05-03. Affine Pieri rule for periodic Macdonald spherical functions and fusion rings. https://doi.org/10.1016/j.aim.2021.108027

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