Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 22 min ago
PreprintarXiv licencearXiv

Characteristic Functions of Parahoric Character Sheaves

  • Zhihang Yu
Open at sourcePDFDOICite

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 GF2 character restricted to GF.

Related

  1. Parahoric motivic Hecke categories in equal and mixed characteristic
    Sebastian Bartling, Rızacan Çiloğlu
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. Characteristic cycles of constructible sheaves and microlocalization
    Takeshi Saito
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Parahoric Spherical Whittaker Functions
    Markos Karameris
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Singular supports, characteristic cycles, and microlocalization of constructible sheaves
    Takeshi Saito, Jiangnan Xiong, Enlin Yang
    arXivPreprintCC0Full textAlgebra & number theoryarXiv
  5. Characteristic cycles and non-acyclicity classes for constructible étale sheaves
    Kaicheng Bao, Jiangnan Xiong, Enlin Yang
    arXivPreprintCC0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{yu2026characteristic,
  title = {{Characteristic Functions of Parahoric Character Sheaves}},
  author = {Zhihang Yu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19860},
  eprint = {2609.19860},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19860},
}
RIS
TY  - UNPB
TI  - Characteristic Functions of Parahoric Character Sheaves
AU  - Zhihang Yu
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.19860
UR  - https://arxiv.org/abs/2609.19860
AB  - 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.
ER  -