Towards a categorical analogue of Gelfand-Kazhdan Theorem
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 $PGL_2(\mathcal{K})$.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2024
- DOI:
- 10.48550/arXiv.2410.02139
- arXiv:
- arXiv:2410.02139
- Bibcode:
- 2024arXiv241002139P
- Keywords:
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- Mathematics - Representation Theory