Abstract
The bispectral quantum Knizhnik–Zamolodchikov (BqKZ) equation corresponding to the affine Hecke algebra H of type A N-1 is a consistent system of q-difference equations which in some sense contains two families of Cherednik’s quantum affine Knizhnik–Zamolodchikov equations for meromorphic functions with values in principal series representations of H. In this paper, we extend this construction of BqKZ to the case where H is the affine Hecke algebra associated with an arbitrary irreducible reduced root system. We construct explicit solutions of BqKZ and describe its correspondence to a bispectral problem involving Macdonald’s q-difference operators.
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Acknowledgments
The author is supported by the Netherlands Organization for Scientific Research (NWO) in the VIDI-project “Symmetry and modularity in exactly solvable models”. He likes to thank Jasper Stokman for his advice and many valuable discussions.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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van Meer, M. Bispectral quantum Knizhnik–Zamolodchikov equations for arbitrary root systems. Sel. Math. New Ser. 17, 183–221 (2011). https://doi.org/10.1007/s00029-010-0039-6
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DOI: https://doi.org/10.1007/s00029-010-0039-6