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Results tagged with algebraic-groups
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user 2024
Algebraic varieties with group operations given by morphisms, or group objects in the category of algebraic varieties, the category of algebraic schemes, or closely related categories.
12
votes
3
answers
1k
views
Is the Gelfand-Graev character isomorphic to a cohomology group for some sheaf on a Deligne-...
Deligne-Lusztig theory
is awesome. You take a maximal torus $T$, you take a character $\theta$, construct a variety $X_T$$^*$, take etale cohomology, get a virtual character $R_T^\theta$, maybe it's …
- 4,593
9
votes
1
answer
444
views
Are affine groups over rings of integers finitely generated?
I'll begin by saying that I'm not sure what I want to ask specifically, but pretty sure what in general, so please don't hold my misunderstandings against me, but do comment on them.
I know that the …
- 4,593
6
votes
1
answer
336
views
Finite field analogue of representations in same packet have equal central character
In Kevin Buzzard's recent question, a warm up question was: if two automorphic representations are nearly equivalent, then are the central characters of their local components equal?
Working my way u …
- 4,593
3
votes
1
answer
246
views
Is this unipotent group, over characteristic 2, connected?
Let $E_{ij}(x)\in \mathrm{Mat}_{7\times7}(\overline{\mathbb{F}}_2)$ be the matrix with zeros everywhere, except for the value $x$ at $ij$. Set $$a(x)=1+E_{12}(x)+E_{34}(x)+E_{56}(x),\quad b(y)=1+E_{23 …
- 4,593
3
votes
1
answer
531
views
Points on Deligne-Lusztig varieties: Interpreting Borels in relative position as flags with ...
Background
I am studying the paper "On the Green polynomials of classical groups" by Lusztig, in which he computes the values of the Deligne-Lusztig representation, corresponding to a Coxeter element …
- 4,593