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- W3100593778 abstract "We use the double affine Hecke algebra of type GL_N to construct an explicit consistent system of q-difference equations, which we call the bispectral quantum Knizhnik-Zamolodchikov (BqKZ) equations. BqKZ includes, besides Cherednik's quantum affine KZ equations associated to principal series representations of the underlying affine Hecke algebra, a compatible system of q-difference equations acting on the central character of the principal series representations. We construct a meromorphic self-dual solution Phi of BqKZ which, upon suitable specializations of the central character, reduces to symmetric self-dual Laurent polynomial solutions of quantum KZ equations. We give an explicit correspondence between solutions of BqKZ and solutions of a particular bispectral problem for the Ruijsenaars' commuting trigonometric q-difference operators. Under this correspondence Phi becomes a self-dual Harish-Chandra series solution Phi^+ of the bispectral problem. Specializing the central character as above, we recover from Phi^+ the symmetric self-dual Macdonald polynomials." @default.
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- W3100593778 date "2009-10-23" @default.
- W3100593778 modified "2023-10-16" @default.
- W3100593778 title "Double Affine Hecke Algebras and Bispectral Quantum Knizhnik-Zamolodchikov Equations" @default.
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- W3100593778 doi "https://doi.org/10.1093/imrn/rnp165" @default.
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