By Ivan Cherednik

This can be an primarily self-contained monograph in an exciting box of primary value for illustration thought, Harmonic research, Mathematical Physics, and Combinatorics. it's a significant resource of normal information regarding the double affine Hecke algebra, often known as Cherednik's algebra, and its outstanding functions. bankruptcy 1 is dedicated to the Knizhnik-Zamolodchikov equations connected to root platforms and their family members to affine Hecke algebras, Kac-Moody algebras, and Fourier research. bankruptcy 2 features a systematic exposition of the illustration thought of the one-dimensional DAHA. it's the least difficult case yet faraway from trivial with deep connections within the thought of exact features. bankruptcy three is ready DAHA in complete generality, together with functions to Macdonald polynomials, Fourier transforms, Gauss-Selberg integrals, Verlinde algebras, and Gaussian sums. This ebook is designed for mathematicians and physicists, specialists and scholars, in case you are looking to grasp the double Hecke algebra procedure. stopover at http://arxiv.org/math.QA/0404307 to learn bankruptcy zero and chosen issues from different chapters.

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