All Questions
Tagged with finite-groups lie-groups
61 questions
1
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167
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Finite groups normalizing a torus
Let $G$ be a semi-simple linear algebraic group over the complex numbers, e.g. the special linear group. Can you find an example of a finite sub-group $H$ of $G$ which does not normalize any maximal ...
- 2,384
3
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0
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128
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Extension of Tits' theorem on groups with a BN-pair of rank ≥ 3
Tits has proved that a finite simple group $G$ with a BN-pair of rank $n \ge 3$, is of Lie type. Let $B$ be the Borel subgroup and $(W,S)$ the Coxeter system. The subset lattice of the set $S$ is ...
8
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666
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Approximating Lie groups by finite groups
How can one approximate compact Lie groups by finite groups?
My wish is something like this:
Let $G$ be a compact Lie group.
There is a sequence of nested finite subgroups $G_n$ so that $G_n\to G$...
- 8,086
1
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1
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274
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The compact Lie group contains a finite subgroup $\mathbb{Z}_{n_1} \times \mathbb{Z}_{n_2} \times \mathbb{Z}_{n_3}$
Given a finite Abelian group: $G=\mathbb{Z}_{n_1} \times \mathbb{Z}_{n_2} \times \mathbb{Z}_{n_3}$, where ${n_1},{n_2},{n_3}$ are arbitrary positive integers. ${n_1},{n_2},{n_3}$ may have or may not ...
- 10.5k
1
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181
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Discrete group action on the sphere
Let $f$ be a continuous function on $S^3$ and let $\xi^{\perp}=\{x\in S^3:\,x\cdot\xi=0\}$
be a two-dimensional equator of $S^3$ orthogonal to the direction $\xi\in S^3$ (here $x\cdot\xi$ stands for a ...
8
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0
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408
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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, ...
- 52.9k
1
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1
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104
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The action of graph automorphism of finite symplectic group on maximal subgroups
Let $G=Sp(4,2^f)$ with $f>1$. Based on the facts when $f$ is small, I would feel the following:
$G$ has two conjugacy classes of subgroups isomorphic to $SO^+(4,2^f)$. One is in Aschbacher's class ...
- 767
3
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0
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572
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How to find the normalizer of a finite subroup in a Lie group?
If a group $G$ is generated by finitely many subgroups $G_i$ and $H$ a subgroup of $G$, under which conditions can $N_G(K)$, the normalizer of $K$ in $G$, be generated by all the normailizers $N_{G_i}(...
- 31
0
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0
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110
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Brauer characters of finite simple group $E_8(5)$
I would like to find the irreducible characters of the group $E_8(5)$ (mod 2)?
Can anyone help? (I am elementary in working with Brauer characters)
Many thanks
- 169
2
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0
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134
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Finite subgroups of compact simple Lie groups [duplicate]
The finite subgroups of $SU(2)$ consist of the symmetry groups of the Platonic solids plus the finite subgroups of $O(2)$. I would like to know if there are any results concerning $SU(3)$. In ...
- 351
2
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123
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Finite subgroups (lattices) in the large N limit of SU(N)
I would like to gain some information about the discrete subgroups (lattices) of SU(N) Lie groups. I have already read some answers and references concerning the N=3 and N=4 cases. I am more ...
- 21