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

Giovanna Carnovale
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Abstract

We work out a theory of integrability on the braided covector Hopf algebra and braided vector Hopf algebra of type A_n as introduced by Kempf and Majid. Starting by their definition of braided Fourier transform we prove n-dimensional analogues to results by Koornwinder expressing the correspondence between products of q^2-Gaussians times monomials and products of q^2-Gaussians times q^2-Hermite polynomials under the transform. We invert the correspondence finding a suitable inverse to the transform, different from that by Kempf and Majid (our integral is not bosonic) and we show that in this case the (q-)Plancherel measure will depend on the parity of the generalized functions that we are transforming.

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Giovanna Carnovale. 1998-10-02. On the braided Fourier transform in the n-dimensional quantum space. https://arxiv.org/abs/math/9810011

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