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The FourierJacobi Map and Small - people ucsc

The FourierJacobi Map and Small - people ucsc 2025

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The thesis by Martin Hillel Weissman explores the Fourier-Jacobi functor applied to smooth representations of split, simple, simply-laced p-adic groups. It draws parallels between representation theory and classical modular forms, particularly focusing on degenerate principal series and small representations. The work includes a detailed analysis of the structure theory of parabolics, the effects of the Fourier-Jacobi map on representations, and the classification of reducibility points in degenerate principal series. The findings contribute to understanding how these mathematical structures relate to arithmetic information encoded in modular forms.

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