DAHA and Fourier transforms

Lundi 31 mai 2010 15:30-00:00 - Cherednik Ivan - Univ. North Carolina

Résumé : The talk is an introduction to the new vintage of the (algebraic) theory of Fourier transform based on its interpretation as transposition of periods of an elliptic curve. Double affine Hecke algebras serve this approach. The key example is actually the clasical 1D Hankel transform in the theory of Bessel functions. It can be interpreted via SL(2,R), but this relation can be hardly extended to other Lie groups. Rational DAHA provide such interpretation for any root systems (and beyond) ; the q-theory includes practically all known « integrable » cases of the Fourier analysis in the range from roots of unity to the theory of elliptic radial parts. I will discuss the Hankel transform and its non-symmetric (also classical) version in detail and then will demonstrate how the q-theory goes (and what is the realtion to the elliptic curves).

Lieu : 425 - 113-115

DAHA and Fourier transforms  Version PDF
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juillet 2020 | septembre 2020