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Results tagged with finite-groups
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user 2024
Questions on group theory which concern finite groups.
1
vote
0
answers
224
views
When is induction to Siegel parabolic of cuspial representation reducible
Hello,
I'm currently looking at the symplectic group $Sp_4(\mathbb{F}_q)$ ($q$ odd), trying to understand some of its comlpex representation theory. I note that it has been completely calculated by …
- 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
6
votes
Navigating $\mathbb{Z}/p\mathbb{Z}$
Let $r$ be the "base" and $x$ the number to represent.
Let $m = \log_{2} (p) + \epsilon$. Construct the matrix $L$:
$$\begin{pmatrix}
x & \lambda & 0 & & ... & & 0 \\\\
1 & 0 & \lambda & & & & 0 \\\ …
- 4,593
12
votes
3
answers
1k
views
Is the Gelfand-Graev character isomorphic to a cohomology group for some sheaf on a Deligne-...
Deligne-Lusztig theory
is awesome. You take a maximal torus $T$, you take a character $\theta$, construct a variety $X_T$$^*$, take etale cohomology, get a virtual character $R_T^\theta$, maybe it's …
- 4,593