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arXiv · 2606.12288

Canonical Bernstein-Zelevinsky Filtration and Casselman's Comparison Conjecture

Kaidi Wu·Jun Yu
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Abstract

We establish a canonical Bernstein--Zelevinsky filtration for Casselman--Wallach representations that is analogous to the $p$-adic case. In addition, we outline an approach to Casselman's comparison conjecture and prove it for general linear groups, as well as for quasi-split even orthogonal groups in some special cases. We also give some applications of the Bernstein--Zelevinsky filtration, such as to the study of highest derivatives and the indecomposability of mirabolic restrictions.

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Kaidi Wu, Jun Yu. 2026-06-10. Canonical Bernstein-Zelevinsky Filtration and Casselman's Comparison Conjecture. https://arxiv.org/abs/2606.12288

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