A discrete Fourier transform associated with the affine Hecke algebra
J. F. van Diejen, E. Emsiz
TL;DR
This paper introduces a new Fourier transform linked to the double affine Hecke algebra of type A1 at q=1, providing a periodic analogue of a classical Fourier transform in algebraic harmonic analysis.
Contribution
It presents an explicit representation of the double affine Hecke algebra at q=1, leading to a novel periodic Fourier transform associated with this algebra.
Findings
Constructed an explicit algebraic representation at q=1
Developed a periodic Fourier transform analogue
Bridged affine Hecke algebra and harmonic analysis
Abstract
We introduce an explicit representation of the double affine Hecke algebra (of type ) at that gives rise to a periodic counterpart of a well-known Fourier transform associated with the affine Hecke algebra.
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