"On the braided Fourier transform in the n-dimensional quantum space"

Abstract

We work out in detail a theory of integrability on the braided covector Hopf algebra and the braided vector Hopf algebra of type An introduced in Ma and KeMa Starting with a denition of braided Fourier transform very similar to that in KeMa we obtain ndimensional analogous results to those in Koo expressing the correspondence between products of the qGaussian gq x times monomials and products of the qGaussian Gq times qHermite polynomials under the transform We invert the correspondence by nding a suitable inversion dierent from that in KeMa We show that with this transforms whenever n the Plancherel measure will depend on the parity of the power series that we are transforming