All Questions
5 questions with no upvoted or accepted answers
8
votes
0
answers
408
views
Connection between two theorems on character values?
In a recent arXiv preprint here, Dipendra Prasad has revisited a 1976 theorem of Kostant (Theorem 2 in the paper On Macdonald's $\eta$-function formula, the Laplacian and generalized exponents, ...
4
votes
0
answers
449
views
Normalizer of a split torus
Let $G$ be a connected reductive group split over a field $k$. Let $T$ be a maximal split torus of $G$. Consider $N_G(T)$, the normalizer of $T$ in $G$, we have $N_G(T)/T \cong W$, the Weyl group of $...
3
votes
0
answers
71
views
Conjugacy classes in reductive group under adjoint action of parabolic subgroup
Given a reductive group $G$ over a finite field and a parabolic subgroup $P$ , I wonder what are the orbits in $G$ under the adjoint action of $P$. This should be standard, but I can only find results ...
2
votes
0
answers
65
views
Are the integer points of a simple linear algebraic group 2-generated?
Set Up:
Let $ K $ be a totally real number field. Let $ \mathcal{O}_K $ be the ring of integers of $ K $. Let $ G $ be a simple linear algebraic group. Suppose that $ G(\mathbb{R}) $ is a compact Lie ...
1
vote
0
answers
161
views
N(H)/H and the Weyl group
Let $ H $ be a connected subgroup of $ G=\mathrm{SU}(n) $ such that $ N_G(H)/H $ is finite. Is $ N_G(H)/H $ always a subgroup of the symmetric group $ \mathrm{S}_n $?
I just noticed this from the ...