A spectral theorem for compact representations and non-unitary cusp forms

Anton Deitmar

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arXiv · 2401.01859

A spectral theorem for compact representations and non-unitary cusp forms

Anton Deitmar

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Abstract

We show that a compact representation of a semisimple Lie group has an orthogonal decomposition into finite length representations. This generalises and simplifies a number of more special spectral theorems in the literature. We apply it to the case of cusp forms, thus settling the spectral theory for the space of non-unitary twisted cusp forms.

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Anton Deitmar. 2024-01-03. A spectral theorem for compact representations and non-unitary cusp forms. https://arxiv.org/abs/2401.01859

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