Questions tagged [deligne-lusztig-theory]
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8
questions with no upvoted or accepted answers
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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 ...
6
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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 ...
6
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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''...
5
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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 $...
4
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$\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{...
4
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92
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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 ...
3
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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 ...
2
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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 ...