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arXiv · 2410.02139

Towards a categorical analogue of Gelfand-Kazhdan Theorem

Alexander Popkovich
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Abstract

A celebrated theorem by Gelfand-Kazhdan states that the restriction of any cuspidal irreducible representations of $GL_n(\mathcal{K})$ over local field to the mirabolic subgroup $P$ is isomorphic to the standard irreducible representation of $P$. We formulate a conjecture that an analogous statement should hold for categorical representations. In this note we prove this for a particular example of an irreducible cuspidal categorical representation of $PGL_2(\mathcal{K})$.

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BibTeXRIS

Alexander Popkovich. 2024-10-03. Towards a categorical analogue of Gelfand-Kazhdan Theorem. https://arxiv.org/abs/2410.02139

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