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# Tag: groups

## Google groups digest mail not displaying correct time?

## How to set a profile picture for the Google Groups Email Address in Google Workspace, so recipients can see the profile picture in their Gmail inbox

## algebraic groups – Explicit smooth representation of $G$ constructed from action of the Hecke algebra $H(G)$

## gmail – gsuite user unable to access google groups

## Representation theory of Chevalley groups as a categorical trace

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

## python – Calculate date difference of dataframe groups

## Workflows within teams or groups

## Social Groups for XenForo | Nulled Scripts Download

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

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The time displayed in the digest mail is "Mar 04 02:56AM"

Whereas the actual time I received the mail is "Mar 04 4:26 pm"

We are using Google Workspace together with Groups for Business as a shared email inbox. The given address info@example.com is also used as the email sender.

When users receive emails from info@example.com they only see the gray profile image only of a human.

We want to have our corporate logo to be visible and a looking for ways on how to set it.

What we tried:

- BIMI: Is currently in closed beta, and need certs that one have to buy.
- Creating a personal Gmail account with info@example.com as the address is not possible. Gmail complains that the email is already in use.
- Gravatar Icon does exist but is not picked up by Gmail.

Are there any other options?

Let $G$ be a unimodular totally disconnected topological group (for instance, the $F$-points of a reductive group over a nonarchimedean local field). Fix a Haar measure $dx$ on $G$, normalized such that $mu(G)=1$. Then one can form the Hecke algebra $H:=H(G)$ to be defined as the convolution algebra of locally constant functions on $G$, where convolution is given by $$f_1star f_2(g) =int_G f_1(x)f_2(x^{-1}g) dx.$$

Note that this algebra is associative, noncommutative, and nonunital. There are smaller rings inside, denoted $H(G)_Ksubset H(G)$, where $K$ is compact open, consisting of $K$-biinvariant functions. Each $H(G)_K$ has units given by $e_K:=text{vol}(K)^{-1}1_K$ where $1_K$ is the characteristic function for $K$. An $H$-module is a $mathbb{C}$-algebra homomorphism $pi: Hto text{End}(V)$. Further, we say that such an $H$-module is **non-degenerate** if for all $vin V$ there exists compact open $K$ such that $e_K(v)=v$ where $e_K(v)$ refers to the action of $e_K$ on $v$.

It is well-known that there is a categorical equivalence between non-degenerate $H$-modules and smooth representations of $G$. For instance, see Bushnell-Henniart. I am trying to realize this correspondence in a more explicitly way. Bushnell-Henniart remarks that given a non-degenerate $H$-module $V$, we can construct a smooth representation of $G$ by taking choosing compact open $K$ such that $e_Kv=v$ and then setting $pi(g)(v):=text{vol}(K)^{-1}1_{gK}(v)$ where the right hand side indicates the action of $H$ on $V$. My confusion is that I do not see how this is a well-defined action. First:

(i) Given $gin G$, Why does $pi(g)(v)$ not depend on the choice of $K$?

(ii) How does one see that $pi(g_1g_2)(v)=pi(g_1)pi(g_2)(v)$?

For (i), certainly this is clear if $g=e$, and the general statement should be similar. But I do not see how to make this work. For (ii), it is clear that one must choose $K$ to be sufficiently small, but the details elude me.

Any and all remarks would be appreciated.

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:

https://groups.google.com/u/2/g/custom-group-name/members

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

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?

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

I have a dataframe where I need to calculate the length of time (in years) between dates of groups. For example, I want the difference between the *first* time a `Name`

–`ID`

group appeared (identified by `%_chng=New`

), and the date in the `Date`

column.

```
df = pd.DataFrame({'Name': {0: 'Faye', 1: 'Faye', 2: 'Faye', 3: 'Faye', 4: 'Faye', 5: 'Faye', 6: 'Faye', 7: 'Mike', 8: 'Mike', 9: 'Mike', 10: 'Mike', 11: 'Mike', 12: 'Mike', 13: 'Mike', 14: 'Mike'}, 'Date': {0: '2020-12-31', 1: '2020-09-30', 2: '2020-06-30', 3: '2018-09-30', 4: '2018-09-30', 5: '2018-09-30', 6: '2018-06-30', 7: '2020-12-31', 8: '2020-09-30', 9: '2020-09-30', 10: '2020-06-30', 11: '2020-03-30', 12: '2019-12-31', 13: '2019-09-30', 14: '2019-06-30'}, 'ID': {0: 'A', 1: 'A', 2: 'A', 3: 'A', 4: 'A', 5: 'B', 6: 'B', 7: 'A', 8: 'A', 9: 'C', 10: 'C', 11: 'C', 12: 'C', 13: 'C', 14: 'C'}, '%_chng': {0: '0.3', 1: '0.2', 2: 'New', 3: '0.1', 4: 'New', 5: '0.2', 6: 'New', 7: '0.7', 8: 'New', 9: '0.1', 10: '0.2', 11: '0.1', 12: '0.4', 13: '0.3', 14: 'New'}})
Name Date ID %_chng
0 Faye 2020-12-31 A 0.3
1 Faye 2020-09-30 A 0.2
2 Faye 2020-06-30 A New
3 Faye 2018-09-30 A 0.1
4 Faye 2018-09-30 A New
5 Faye 2018-09-30 B 0.2
6 Faye 2018-06-30 B New
7 Mike 2020-12-31 A 0.7
8 Mike 2020-09-30 A New
9 Mike 2020-09-30 C 0.1
10 Mike 2020-06-30 C 0.2
11 Mike 2020-03-30 C 0.1
12 Mike 2019-12-31 C 0.4
13 Mike 2019-09-30 C 0.3
14 Mike 2019-06-30 C New
```

So the expected output would look something like:

```
Name Date ID %_chng date_length
0 Faye 2020-12-31 A 0.3 0.50
1 Faye 2020-09-30 A 0.2 0.25
2 Faye 2020-06-30 A New 0.00
3 Faye 2018-09-30 A 0.1 0.25
4 Faye 2018-09-30 A New 0.00
5 Faye 2018-09-30 B 0.2 0.25
6 Faye 2018-06-30 B New 0.00
7 Mike 2020-12-31 A 0.7 0.25
8 Mike 2020-09-30 A New 0.00
9 Mike 2020-09-30 C 0.1 1.25
10 Mike 2020-06-30 C 0.2 1.00
11 Mike 2020-03-30 C 0.1 0.75
12 Mike 2019-12-31 C 0.4 0.50
13 Mike 2019-09-30 C 0.3 0.25
14 Mike 2019-06-30 C New 0.00
```

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…

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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.

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