Appears in collection : 2025 - T1 - WS1 - Intertwining operators and geometry

The $(k, a)$-generalized Fourier transform $\mathscr{F}_{k, a}$ 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 $a > 0$.