By Ivan Cherednik

This can be a designated, primarily self-contained, monograph in a brand new box of primary value for illustration concept, Harmonic research, Mathematical Physics, and Combinatorics. it's a significant resource of common information regarding the double affine Hecke algebra, also referred to as Cherednik's algebra, and its striking functions. bankruptcy 1 is dedicated to the Knizhnik-Zamolodchikov equations hooked up to root platforms and their relatives to affine Hecke algebras, Kac-Moody algebras, and Fourier research. bankruptcy 2 includes a systematic exposition of the illustration conception of the one-dimensional DAHA. it's the easiest case yet faraway from trivial with deep connections within the concept of unique services. 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 booklet is designed for mathematicians and physicists, specialists and scholars, in case you are looking to grasp the recent double Hecke algebra strategy.

Continue reading "Double Affine Hecke Algebras by Ivan Cherednik"