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arXiv · 2509.18442

An alternative construction of character sheaves on parahoric subgroups

Alexander B. Ivanov·Sian Nie·Zhihang Yu
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Abstract

Inspired by the foundational work of Bezrukavnikov and Chan \cite{BC24} on character sheaves for parahoric subgroups and an alternative interpretation of deep level Deligne-Lusztig characters in \cite{Nie_24}, we present a parallel but closed (non-iterated) construction of character sheaves within the framework of J.--K. Yu's types. We show that our construction yields perverse sheaves, which coincide with those produced in \cite{BC24} in an iterated way. In the regular case we establish the compatibility of their Frobenius traces with deep level Deligne-Lusztig characters. As an application, we prove the positive-depth Springer's hypothesis for arbitrary characters, thereby generalizing the generic case result of Chan and Oi \cite{CO25}. The proofs of our results make critical use of the strategies and results from \cite{BC24} and \cite{Nie_24}.

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Alexander B. Ivanov, Sian Nie, Zhihang Yu. 2025-09-22. An alternative construction of character sheaves on parahoric subgroups. https://arxiv.org/abs/2509.18442

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