Intertwining operators and geometry

(k,a)-generalized Fourier transform with negative a

23 janv. 2025, 16:30

40m

Amphithéâtre Hermite (Institut Henri Poincaré)

Orateur

Tatsuro Hikawa (The University of Tokyo)

Description

The $(k,a)$-generalized Fourier transform ${\mathcal{F}}_{k,a}$ introduced by Ben Saïd--Kobayashi--Ørsted is a deformation family of the classical Fourier transform with a Dunkl parameter $k$ and a parameter $a>0$ that interpolates minimal representations of two different simple Lie groups. In this session, we will talk about some new results when $a$ is not positive. As a main result, we find a unitary transform that intertwines the known case $a>0$ and the new case $a<0$.