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

The $(k, a)$-generalized Fourier transform Fk, a introduced by Ben Sa\"id--Kobayashi--{}rsted is a deformation family of the classical Fourier transform F with the Dunkl parameter k and the parameter $a > 0$ that interpolates minimal representations of two different simple Lie groups. In the present paper, we focus on the case $a < 0$. As a main result, we find a unitary transform that intertwines the known case $a > 0$ and the new case $a < 0$.