Year: 2026
Type: preprint
Abstract: We establish a Jordan decomposition formula for the characteristic functions of the character sheaves on parahoric subgroups defined in \cite{INY25}. For a sufficiently large $q$, these functions are $(-1)^{\dim G}$ times the corresponding deep level Deligne--Lusztig characters, extending \cite{Lu90} to positive depth. We also prove the orthogonality for the generalized deep level Green functions and the character sheaves functions. Moreover, we obtain an explicit expression of characteristic functions of simple character sheaves. As an application, we present a sheaf-theoretic expression to the multiplicity of the $G^{F^2}$ character restricted to $G^{F}$.
Source: arXiv (Cornell University)
Author: Yu, Zhihang
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213611014
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