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arXiv · 2001.11414

Fourier transform as a triangular matrix

G. Lusztig
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Abstract

Let V be a finite dimensional vector space over the field with two elements with a given nondegenerate symplectic form. Let [V] be the vector space of complex valued functions on V and let [V]_Z be the subgroup of [V] consisting of integer valued functions. We show that there exists a Z-basis of [V]_Z consisting of characteristic functions of certain explicit isotropic subspaces of V such that the matrix of the Fourier transform from [V] to [V] with respect to this basis is triangular. We show that this is a special case of a result which holds for any two-sided cell in a Weyl group.

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G. Lusztig. 2020-01-30. Fourier transform as a triangular matrix. https://arxiv.org/abs/2001.11414

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