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arXiv · 2404.19210

Character Sheaves on Reductive Lie Algebras in Positive Characteristic

Tong Zhou
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Abstract

We prove a microlocal characterisation of character sheaves on a reductive Lie algebra over an algebraically closed field of sufficiently large positive characteristic: a perverse irreducible G-equivariant sheaf is a character sheaf if and only if it has nilpotent singular support and is quasi-admissible. We also present geometric proofs, in positive characteristic, of the equivalence between being admissible and being a character sheaf, and various characterisations of cuspidal sheaves, following the work of Mirkovi\'c.

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BibTeXRIS

Tong Zhou. 2024-04-30. Character Sheaves on Reductive Lie Algebras in Positive Characteristic. https://doi.org/10.1093/imrn%2Frnae221

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