{"ID":23510313,"CreatedAt":"2026-09-18T02:21:44.056544415Z","UpdatedAt":"2026-09-18T02:21:44.056544415Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.19860","arxiv_id":"2609.19860","title":"A Comparison Theorem for Parahoric Character Sheaves","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. As an application, we present a sheaf-theoretic expression to the multiplicity of the $G^{F^2}$ character restricted to $G^{F}$.","short_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....","url_abs":"https://arxiv.org/abs/2609.19860","url_pdf":"https://arxiv.org/pdf/2609.19860v1","authors":"[\"Zhihang Yu\"]","published":"2026-09-17T08:13:35Z","proceeding":"math.RT","tasks":"[\"math.RT\"]","methods":"[]","has_code":false}