Affine Pieri rule for periodic Macdonald spherical functions and fusion rings

Journal article (2021)

Authors

Jan Felipe van Diejen University of Talca
E. Emsiz Applied Probability - EEMCS
I. N. Zurrián Universidad Nacional de Córdoba
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2021 J.F. van Diejen, E. Emsiz, I.N. Zurrián
DOI
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https://doi.org/10.1016/j.aim.2021.108027
Affine Hecke algebras Affine Lie algebras Macdonald spherical functions Wess-Zumino-Witten fusion rings
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Published Date

2021

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

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.