Orateur
Tatsuro Hikawa
(The University of Tokyo)
Description
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 $.
