Seminar of Department of Algebra and Geometry - George Lusztig (24.5.2024)

Friday 24.5.2024 at 11:00, Lecture room C

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George Lusztig (MIT):
Fourier transform as a triangular matrix

Abstract: 
Fourier transform is an isomorphism of order 4 from the vector space of square integrable functions on real numbers to itself. In late 1800's Hermite described a complete set of eigenvectors of this linear map (involving the Hermite polynomials). We can replace this vector space by the vector space of complex valued functions on a vector space of dimension 2n over the field with two elements with a nondegenerate symplectic form. This vector space has again a natural Fourier transform which plays a role in the study of representations of finite groups of Lie type. We are interested in proving an analogue of Hermite's results in this context. But now instead of making the matrix of Fourier transform diagonal we will make it only triangular.

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