Conjugacy classes of stabilizer subgroups
$begingroup$
Let $Gsubseteq GL(V)$ be a complex finite reflection group. I would like to understand the stabilizer subgroups of $G$, and their normalizers. By this I mean (the conjugacy classes of) subgroups $H<G$ such that there exists $vin V$ such that $Stab_G(v)=H$, together with $N_G(H)$.
Ideally there would be some table somewhere, with the poset of stabilizer subgroups. I was able to compute everything (rather painfully) when $dim(V)leq 3$ or when $G=G(n,m,p)$, so I am only missing the exceptional groups of rank at least $4$, that is 28-37 in this list (Shephard-Todd classification).
Alternatively, since I am also trying to learn to use Magma/Sage/GAP, I was wondering if there is a way to extract the information I need from these programs.
group-theory finite-groups gap reflection
asked Nov 30 '18 at 8:38
CehijuCehiju
464
$endgroup$
add a comment |
$begingroup$
Let $Gsubseteq GL(V)$ be a complex finite reflection group. I would like to understand the stabilizer subgroups of $G$, and their normalizers. By this I mean (the conjugacy classes of) subgroups $H<G$ such that there exists $vin V$ such that $Stab_G(v)=H$, together with $N_G(H)$.
Ideally there would be some table somewhere, with the poset of stabilizer subgroups. I was able to compute everything (rather painfully) when $dim(V)leq 3$ or when $G=G(n,m,p)$, so I am only missing the exceptional groups of rank at least $4$, that is 28-37 in this list (Shephard-Todd classification).
Alternatively, since I am also trying to learn to use Magma/Sage/GAP, I was wondering if there is a way to extract the information I need from these programs.
group-theory finite-groups gap reflection
asked Nov 30 '18 at 8:38
CehijuCehiju
464
$endgroup$
add a comment |
$begingroup$
Let $Gsubseteq GL(V)$ be a complex finite reflection group. I would like to understand the stabilizer subgroups of $G$, and their normalizers. By this I mean (the conjugacy classes of) subgroups $H<G$ such that there exists $vin V$ such that $Stab_G(v)=H$, together with $N_G(H)$.
Ideally there would be some table somewhere, with the poset of stabilizer subgroups. I was able to compute everything (rather painfully) when $dim(V)leq 3$ or when $G=G(n,m,p)$, so I am only missing the exceptional groups of rank at least $4$, that is 28-37 in this list (Shephard-Todd classification).
Alternatively, since I am also trying to learn to use Magma/Sage/GAP, I was wondering if there is a way to extract the information I need from these programs.
group-theory finite-groups gap reflection
asked Nov 30 '18 at 8:38
CehijuCehiju
464
$endgroup$
Let $Gsubseteq GL(V)$ be a complex finite reflection group. I would like to understand the stabilizer subgroups of $G$, and their normalizers. By this I mean (the conjugacy classes of) subgroups $H<G$ such that there exists $vin V$ such that $Stab_G(v)=H$, together with $N_G(H)$.
Ideally there would be some table somewhere, with the poset of stabilizer subgroups. I was able to compute everything (rather painfully) when $dim(V)leq 3$ or when $G=G(n,m,p)$, so I am only missing the exceptional groups of rank at least $4$, that is 28-37 in this list (Shephard-Todd classification).
Alternatively, since I am also trying to learn to use Magma/Sage/GAP, I was wondering if there is a way to extract the information I need from these programs.
group-theory finite-groups gap reflection
group-theory finite-groups gap reflection
asked Nov 30 '18 at 8:38
CehijuCehiju
464
asked Nov 30 '18 at 8:38
CehijuCehiju
464
edited Nov 30 '18 at 18:25
Cehiju
asked Nov 30 '18 at 8:38
CehijuCehiju
464
asked Nov 30 '18 at 8:38
CehijuCehiju
464
asked Nov 30 '18 at 8:38
CehijuCehiju
464
464
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3019830%2fconjugacy-classes-of-stabilizer-subgroups%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3019830%2fconjugacy-classes-of-stabilizer-subgroups%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown