Questions tagged [deligne-lusztig-theory]

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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 ...
Sasha's user avatar
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6 votes
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cuspidal unipotent representation in small characteristic

Let $\mathbb{F}_q$ be a finite field with $q=p^r$ and $p$ prime. Let $G$ be a connected reductive group over $\mathbb{F}_q$. Is there a difference between the theory of unipotent cuspidal ...
Q. Zhang's user avatar
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An analogue of Deligne--Lusztig theory for real groups?

I am considering the following analogue of Deligne--Lusztig theory: Take e.g. $G=GL_n(\mathbb{C})$, and let $F$ be the complex conjugate, then we have $G^F=GL_n(\mathbb{R})$. Consider the ``Lang map''...
user148212's user avatar
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Deligne-Lusztig and Character sheaves

Consider: $G$ - a nice group ($GL_n$) over a finite field $F$. $X$ - the flag variety. Consider a nice $G$-equivariant $l$-adic sheaf $\mathcal{M}$ on $X \times X$, equipped with Weil structure. Fix $...
Sasha's user avatar
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4 votes
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$\ell$-adic cohomology of a quotient by group action

Suppose $Y \to Y/G$ is the Galois cover induced from a finite group $G$ acting on a scheme $Y$ and that this is indeed a Galois cover with $Y/G$ a scheme. In my case $Y$ is the Drinfeld curve $\mathrm{...
TCiur's user avatar
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Rank and unipotent support

Let $G$ be a finite group of Lie type. I would like to be able to compute the rank (introduced by Howe and Gurevich in "Small representations of finite classical groups") of an irreducible ...
J. Epequin's user avatar
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Duals of unipotent characters of classical finite groups of Lie type in terms of Lusztig's symbols

The irreducible unipotent characters of classical finite groups of Lie type have been classified by Lusztig using the combinatorical notion of "symbols", see "Irreducible ...
Suzet's user avatar
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Relative position of Borel subgroups for the symplectic group

Background Let $n$ be a positive integer, let $W$ be the Weyl group of $\text{GL}_n$. Its set of Borel subgroups is isomorphic to the full flag variety $\mathcal{F}_n$. In this question, I studied ...
EJB's user avatar
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