# Questions tagged [character-sheaves]

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### Existence of an open set with specific properties

I am currently reading Gerard Laumon's Faisceaux caractères, which details various constructions and properties of character sheaves on a connected reductive group $G$ over $\overline{\mathbb{F}}_p$. ...

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### Characteristic functions of character sheaves on tori

I am currently reading a set of lecture notes by V. Ostrik and G. Williamson, Character sheaves, tensor categories and non-Abelian Fourier transform. In Theorem 1.1, they make the assertion that the ...

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### Definition 2.3 in Lusztig's "Character Sheaves I"

About Definition 2.3 in Character Sheaves I: We have the usual $G$, $B$, $T$, Weyl group $W$ and roots $R$. Lusztig wrote down a definition of $R_{\mathcal{L}}$ as:
$$R_{\mathcal{L}}=\{\alpha\in R\;|\;...

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### semisimple support of character sheaves

So the essential question is:
How should we think about, or if possible compute, the semisimple
support of a cuspidal character sheaf?
For example, let $G=SL_2$. We have the cuspidal character ...

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### Naive question about classification of unipotent character sheaves

Let $G$ be a connected reductive algebraic group over (say) $\mathbb{C}$. The set $\hat{G}_u$ of isomorphism classes of unipotent irreducible character sheaves has some complicated classification in ...