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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, ...
Jim Humphreys's user avatar
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 $...
Shawn's user avatar
  • 453
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 ...
Simon Lentner's user avatar
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 ...
Ian Gershon Teixeira's user avatar
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 ...
Ian Gershon Teixeira's user avatar