## gmail – gsuite user unable to access google groups

I’m an Owner of Google Groups instance with two different email accounts – my personal one (gmail.com) and my work one (mycompany.com).

I can verify that my mycompany.com email is an Owner on this page:

BUT when I try to access the Google Groups instance with my mycompany.com email I get this error:

Content unavailable

Try switching accounts, or check with your organization’s administrator to make sure you have permission

mycompany.com’s email is done through GSuite. I’m an GSuite admin (but not a super admin) for mycompany.com.

Maybe there’s a setting in that GSuite that isn’t letting me be a member of a Groups external to the domain of mycompany.com? If so where would I find that setting?

Like I can add new accounts and remove new accounts and I can change (some) people’s OU’s but I don’t see an “Admin roles and privileges” button when I pull up a user account in GSuite. Maybe that’s where I’d normally be able to do this? I can add and remove Apps if that helps idk

## Representation theory of Chevalley groups as a categorical trace

Dennis Gaitsgory’s 2016 preprint, From Geometric to Function-Theoretic Langlands (or How to Invent Shtukas) includes in the third section a very compressed but suggestive discussion of the representation theory of Chevalley groups, using a categorified version of the Grothendieck’s faisceaux-functions correspondence. Particularly, if $$G$$ is a reductive algebraic group (say, $$GL_2$$), their setup allows making sense of the notion that the category $$textrm{Rep}_{G(mathbb{F}_q)}$$ is the categorified ‘trace of Frobenius’ on the 2-category of categorified representations of $$G$$, defined as some kind of module categories over the monoidal category of sheaves on $$G$$ under convolution. I am suppressing some difficulties here, for example all of the categories under consideration are derived, and the flavour of sheaf theory is a bit difficult to pin down.

At the end of a few pages, he is able to derive a seemingly nontrivial observation connecting an object of Springer’s theory to Deligne-Lusztig representations. I don’t understand it.

I’m led to understand there has been some serious progress on at least the formal aspect, for example the 2020 preprint of Gaitsgory-Kazhdan-Rozenblyum-Varshavsky, A toy model for the Drinfeld-Lafforgue shtuka construction offers a much expanded discussion of the formal setup, but without the application to Chevalley groups.

At last, here is a question: has anyone developed this approach to the representation theory of finite groups beyond the very compressed discussion in the 2016 preprint? Of course this theorem is not the target of either paper and people have their eyes set on bigger game, but I would love to read something about this example. Has anyone written about it at length in the last 5 years?

## gr.group theory – Explicit abelianization functor for groups

Assume that I have a short exact sequence of finitely presented groups $$1 longrightarrow K longrightarrow H longrightarrow G longrightarrow 1,$$ where $$G$$ is finite (but I do not know whether this is relevant for what follows). Applying abelianization, we get an exact sequence $$K_{mathrm{ab}} longrightarrow H_{mathrm{ab}} to G_{mathrm{ab}} longrightarrow 0.$$

I would like to have a “quantitative” measure of the lack of left-exactness for the above sequence. For instance, I would like to know if it is possible to find an explicit sequence $${L_i}$$ of groups giving a long exact sequence of the form $$ldots longrightarrow L_3 longrightarrow L_2 longrightarrow L_1 longrightarrow K_{mathrm{ab}} longrightarrow H_{mathrm{ab}} to G_{mathrm{ab}} longrightarrow 0.$$

By “explicit” I mean (for instance) that it is, at least in principle, possible to find presentations for the $$L_i$$ once one has presentations for $$K$$, $$H$$, $$G$$.

Since the category of groups is not abelian (or even additive) we can not perform the usual construction of the derived functors for the abelianization functor. I am aware that some more refined constructions have been presented (cotangent complex, André-Quillen homology, etc, see for instance the comments to this MSE question) but they look very technical and perhaps overkill in the simple case I have in mind.

I am not an expert, but it seems to me that for the case of groups there should be some more down-to-earth construction, related to the usual group (co)homology, but I looked in some standard textbooks and I did not find any. So, let me ask the following

Question. Is it possible to construct groups $$L_i$$ as above in some explicit and in principle computable way? If so, what are some
references?

## Tits reductive groups over local fields, 1.15/3.11. Problem with affine root subgroups of \$SU_3\$ ramified, residue characteristic p=2

Let $$L/K$$ be ramified quadratic extension of local fields, and let characteristic of the residue field of $$K$$ be $$2$$. Let $$mathbb{G}=SU_3$$, $$G=mathbb{G}(K)$$. Let $$text{val}$$ be a valuation on $$K$$ so that $$text{val}(K^times) = mathbb{Z}$$ (and $$text{val}(L^times) = frac{1}{2}mathbb{Z}$$).

Following Tits 1.15 and 3.11, I have been trying to work out the parahoric subgroups of $$G$$ attached to the special vertices $$nu_0$$ and $$nu_1$$ in the building of $$G$$.

Firstly, I’ll start with a description of the root subgroups of $$G$$. I’m using a slightly different notation from Tits’. Let $$u_+(c,d) = begin{pmatrix} 1 & -bar{c} & d \ 0 & 1 & c \ 0 & 0 & 1 end{pmatrix},$$
with $$bar{c}c+d+bar{d}=0$$.
Similarly, $$u_-(c,d) = begin{pmatrix} 1 & 0 & 0 \ c & 1 & 0 \ d & -bar{c} & 1 end{pmatrix},$$
with $$bar{c}c+d+bar{d}=0$$.

We have the root subgroups $$U_{pm a}(K) = { u_pm(c,d) text{ : } c,d in L }$$ and $$U_{pm 2a} = { u_pm(0,d) text{ : } d in L}$$.

Tits later defines $$delta = sup{text{val}(d) text{ : } d in L, , bar{d}+d+1=0}$$. $$delta=0$$ in the unramified case and in the ramified, residue characteristic $$pneq 2$$ case. However, when $$L/K$$ is ramified with residue characteristic $$2$$, $$delta$$ is strictly negative.

From here, Tits finds the set of affine roots of $$G$$ as $$Big{pm a + frac{1}{2}mathbb{Z} +frac{delta}{2}Big} cup Big{pm 2a +mathbb{Z}+ frac{1}{2} + delta Big}.$$

Affine root subgroups are given by $$U_{pm a + gamma/2} = { u_pm(c,d) text{ : } text{val}(d) geq gamma},$$
$$U_{pm 2a+ gamma} = { u_pm(0,d) text{ : } text{val}(d) geq gamma}.$$

The special points $$nu_0$$ and $$nu_1$$ i the standard apartment are defined by $$a(nu_1)=frac{delta}{2}, , a(nu_0) = frac{delta}{2} + frac{1}{4}.$$

From here, one can find that $$G_{nu_1} = langle T_0, U_{a-frac{delta}{2}}, U_{-a+frac{delta}{2}}, U_{2a+frac{1}{2}-delta}, U_{-2a+frac{1}{2}+delta} rangle,$$
$$G_{nu_0} = langle T_0, U_{a-frac{delta}{2}}, U_{-a+frac{1}{2}+frac{delta}{2}}, U_{2a-frac{1}{2}-delta}, U_{-2a+frac{1}{2}+delta} rangle.$$

In 3.11, Tits takes a $$lambda in L$$ with $$text{val}(lambda) = delta$$, satisfying $$lambda+bar{lambda}+1=0$$ in a way such that $$lambda varpi_L + overline{(lambda varpi_L)}=0$$ for some uniformizer $$varpi_L$$ of the ring of integers $$mathcal{O}_L$$ of $$L$$.

In 3.11, Tits defines the lattices $$Lambda_{nu_1} = mathcal{O}_L oplus mathcal{O}_L oplus lambdamathcal{O}_L,$$
$$Lambda_{nu_0} = varpi_L^{-1}mathcal{O}_L oplus mathcal{O}_L oplus lambdamathcal{O}_L.$$ Let $$P_{nu_1}$$ and $$P_{nu_0}$$ be their respective stabilizers.
Tits then states that $$G_{nu_i} = P_{nu_i} cap G_{nu_i}$$ for $$i=0,1$$.

Here’s where my problem comes in.

Consider $$G_{nu_1} = langle T_0, U_{a-frac{delta}{2}}, U_{-a+frac{delta}{2}}, U_{2a+frac{1}{2}-delta}, U_{-2a+frac{1}{2}+delta} rangle.$$ The stabilizer of the lattice $$Lambda_{nu_1}$$ in $$GL_3(L)$$ has the form
$$begin{pmatrix} mathcal{O}_L & mathcal{O}_L & mathfrak{p}_L^{-2delta} \ mathcal{O}_L & mathcal{O}_L & mathfrak{p}_L^{-2delta} \ mathfrak{p}_L^{2delta} & mathfrak{p}_L^{2delta} & mathcal{O}_L end{pmatrix}.$$
Since $$text{val}(delta) < 0$$, intersecting this stabilizer with $$G$$ would give us a matrix roughly looking like
$$begin{pmatrix} mathcal{O}_L & mathfrak{p}_L^{-2delta} & mathfrak{p}_L^{-2delta} \ mathcal{O}_L & mathcal{O}_L & mathfrak{p}_L^{-2delta} \ mathfrak{p}_L^{2delta} & mathcal{O}_L & mathcal{O}_L end{pmatrix},$$

Presumeably, this would tell us that $$U_{a-frac{delta}{2}} = { u_+(c,d) text{ : } c,d in L, , text{val}(d) geq -delta textbf{ and } text{val}(c) geq -delta },$$
$$U_{-a+frac{delta}{2}} = {u_{-}(c,d) text{ : } c,d in L, , text{val}(d) geq delta textbf{ and } text{val}(c) geq 0 }.$$
Normally, one would expect that if $$text{val}(d) = gamma$$, then $$text{val}(d) = frac{gamma}{2}$$ or $$frac{gamma}{2}+frac{1}{4}$$, as whether $$gamma in mathbb{Z}$$ or just $$frac{1}{2}mathbb{Z}$$.

I cannot work out algebraically why we have these improved bounds on the valuation of $$c$$ for these affine root subgroups. I assume it involves some manipulation with $$lambda$$, but I am not making any progress.

Thank you

## powershell – Add and delete Sharepoint Groups from site

Thanks for you time reading this.
We are a Technical School that’s using Sharepoint 365 as way to collect files and resources. We have to open a Sharepoint to each class and I’m compiling a Powershell script to be easier…
When added a Site lets say “Class.ABC”, the system also creates a group called “ClassABC@acme.org” (without the dot) and through the script I add the students to the group. I’m using PNP.Powershell. One example:

The problem is this group “ClassABC@acme.org” is put in the “Members” group of the site by default, and therefore with contribute permissions. I want to change this group to “Visitors” of the site.

I’ve try this:

Remove-PnPGroupMember -LoginName "ClassABC@acme.org" -Identity "Members of Class.ABC"

But it didn’t work as they work only with users not groups!

Is there any way to accomplish this?

Thanks a lot for your kind help. I’m not very good at Powershell, so please be gentle! 😉

## views – Workflows within teams or groups

How I go about implementing editorial workflows within a group of users?
I have user identified with a taxonomy term, for example, a per country or per team-based group.

To simplify configuration and avoid adding more extensions, I went about creating a taxonomy, e.g. “Groups”, within that I have the groups, e.g. “Group A” and “Group B” and then each user is related to that group through a field in the user Account Settings.

Team A

• John Doe – role: Author – taxonomy: Team A
• Jane Doe – role: Reviewer – taxonomy: Team A

Team B

• Jake Ryan – role: Author – taxonomy: Team B
• Joane Ryan – role: Reviewer – taxonomy: Team B

My objective is that when John Doe creates content, the workflow only emails the Reviewer of that group: Jane Doe.

I do struggle to understand the group module. From what I’ve heard about it, I guess it would solve all my problems, but I’m having a lot of difficulties finding information (tutorials, documentation) that would allow me to grasp all the concepts this module introduces.

This is a complete, fully configurable social group system that allows for group discussions, forums, event calendars and a basic group photo album.

The ability to create each section of the group is fully usergroup permissions based. So if you don’t want a user group to create a photo album, you just turn off that ability.

FEATURES :

• Create Group Forum
• Create Group Discussion area*
• Create Group Photo Album (with photo comments)
• Create Group Event Calendar…

.(tagsToTranslate)xenforo(t)xenforo themes(t)xenforo nulled(t)xenforo free(t)xenforo 2.2(t)nulled(t)nulled script(t)whmcs(t)whmcs nulled(t)scripts(t)nulled scripts(t)vbulletin(t)vbulletin nulled(t)vbulletin 5 nulled(t)xenforo resources(t)wordpress download(t)wordpress nulled forum

## list manipulation – How to judge whether two groups of sequences are equal in cycles?

There’s a set of arrays that I want to remove repeated elements that are equal after rotation:

arr = {{1, 2, 3, 4, 5}, {2, 3, 4, 5, 1}, {5, 1, 2, 3, 4}, {4, 3, 2, 5,1}};

The elements {1, 2, 3, 4, 5}, {2, 3, 4, 5, 1}and {5, 1, 2, 3, 4}are the same after operation RotateLeft. I want to delete the duplicate elements and only get {1, 2, 3, 4, 5} and {4, 3, 2, 5, 1}.

DeleteDuplicates[arr, RotateLeft[#1] == #2 &]

However, the above operation can only delete the elements that are equal after one shift.

## Site Permissions and new groups

First of all, why playing with the SharePoint groups that way? You have 3 main ways to provide users with access to the site, using Owners, Members and Visitors (When you click on SharePoint). I wouldn’t go in the advanced mode and create more groups the way we used to do with SharePoint server, rather I’d add people I want to an Office 365 group (or Azure security group) and then invite them to my site and provide them permissions through the Share link.

This is the better way to do it, remember when you want to use more advanced stuff in SharePoint, such as Audience Targeting, it will work only with M365 Groups or Security Groups.

Keep it simple, and feel free to add these users to other M365 groups as needed (or if you prefer, Security Groups) then add them back to your site using the Share link.

## How to organize GameObjects into logical groups in a Unity Scene?

Obviously there are a Scene hierarchy, but the problem is that the scene hierarchy was not meant for organizing GameObjects because parent GameObjects affect the transformation of their children.

For example what can one do to select all the decoration GameObjects? Some might be children of non-decoration GameObjects and buried very deep in the scene hierarchy while others might be root GameObjects.

One solution could be to add a Tag, but since Unity restrict you to only one tag per GameObject, that makes the usage of tags pointless as I have different overlapping categories.

Another solution would be to name objects but that is very error prone as a typing mistake will loose my GameObject. Also the team need to memorize possible tokens in the name which allow even more room for human errors.

Another solution would be to add an identifying Component, similar to how tags work in most other applications. But will there be a penalty in build time/runtime in a large project because of the additional Scripts (Components)?

Any other ideas how I can organize my Scene so that I can easily select a logical group of GameObjects from different unrelated parents in the editor Scene or Hierarchical view?