Affine Pieri rule for periodic Macdonald spherical functions and fusion rings
J.F. van Diejen (University of Talca)
E. Emsiz (TU Delft - Electrical Engineering, Mathematics and Computer Science)
I.N. Zurrián (Universidad Nacional de Córdoba)
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Abstract
Let gˆ be an untwisted affine Lie algebra or the twisted counterpart thereof (which excludes the affine Lie algebras of type BCˆn=A2n(2)). We present an affine Pieri rule for a basis of periodic Macdonald spherical functions associated with gˆ. In type Aˆn−1=An−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 slˆ(n)c-Wess-Zumino-Witten conformal field theories.
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