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

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.

dnd 5e – Does Mind whip prevent bonus actions if you take away an action?

The text for mind whip states

You psychically lash out at one creature you can see within range. The target must make an Intelligence saving throw. On a failed save, the target takes 3d6 psychic damage, and it can’t take a reaction until the end of its next turn. Moreover, on its next turn, it must choose whether it gets a move, an action, or a bonus action; it gets only one of the three. On a successful save, the target takes half as much damage and suffers none of the spell’s other effects

Meanwhile, the rules state

[…] anything that deprives you of your ability to take actions also prevents you from taking a bonus action.

If the target chooses a bonus action, it technically shouldn’t be able to do so, as it was deprived of its action. Or is this a case of specific beats general?

how to reference external file in custom ribbon action using CSOM (JSOM)?

Environment: SharePoint 2013

I am using this script to add a custom action button. There are a few things which I would like to achieve:

1- how can I externalize javascript into a file and call a method defined in that file from commandAction like this:
CommandAction="javascript:myFunction();"

2- how can I delete this custom action button from the ribbon? I do not want it to be hidden.

3- how can I target File tab in Document Library?

<script language="javascript" type="text/javascript" src="//ajax.googleapis.com/ajax/libs/jquery/1.8.1/jquery.min.js"></script>  
<script language="javascript" type="text/javascript">  
    $(document).ready(function() {  
        SP.SOD.executeOrDelayUntilScriptLoaded(AddCustomUserAction, "sp.js");  
    });  
    var oListItem;  
  
    function AddCustomUserAction() {  
        //Get the client context and list object  
        var context = new SP.ClientContext.get_current();  
        var list = context.get_web().get_lists().getByTitle("Check List");  
        //Get the custom user action collection and add the user action  
        var customUserAction = list.get_userCustomActions().add();  
        //Set the location of the user action  
        customUserAction.set_location('CommandUI.Ribbon.ListView');  
        //Add the properties for the custom action  
        var userActionExtension = '<CommandUIExtension xmlns="http://schemas.microsoft.com/sharepoint/">' + '<CommandUIDefinitions>' + '<CommandUIDefinition Location="Ribbon.List.CustomizeList.Controls._children">' + '<Button Id="Ribbon.Documents.New.RibbonTest" ' + 'Command="Notify" ' + 'Sequence="0" ' + 'Image16by16="/_layouts/images/NoteBoard_16x16.png" ' + 'Image32by32="/_layouts/images/NoteBoard_32x32.png" ' + 'Description="Shows the ID of the current list." ' + 'LabelText="Show List ID" ' + 'TemplateAlias="o1"/>' + '</CommandUIDefinition>' + '</CommandUIDefinitions>' + '<CommandUIHandlers>' + '<CommandUIHandler Command="Notify" ' + 'CommandAction="javascript:SP.UI.Notify.addNotification('ListId={ListId}');" />' + '</CommandUIHandlers>' + '</CommandUIExtension>';  
        //Add the command UI extension and update the custom user action  
        customUserAction.set_commandUIExtension(userActionExtension)  
        customUserAction.update();  
        //Load the client context and execute the batch  
        context.load(list, 'UserCustomActions');  
        context.executeQueryAsync(function() {  
            console.log("Custom User Action added successfully to ribbon.");  
        }, function(sender, args) {  
            console.log(args.get_message());  
        });  
    }  
</script>  

dnd 5e – If I ready a action (spell) in response to a companion’s attack, what is a fair GM rulling over the order of events?

In our campaign, I have a cleric who wished to use Ready an Action as his move. His idea behind this was that he wanted to ready Guiding Bolt and the condition he set was that, when one of the player (fighter) attacked a creature (one of 2 trolls), he would release the bolt beforehand. Therefore the figther would have advantage on her attack if the Guiding Bolt hit first.

I ruled that the fighter hit first, but I’m not so sure now – and feel like I was unfair in my ruling, maybe.

I can see both points of view:

  1. If I was the cleric readying my spell, I would cast the spell as soon as I noticed my fighter’s companion intention to attack a creature.

  2. But, also if I’m the fighter and I’m 5′ away from a creature, maybe my attack would land first, before the Guiding Bolt.

I would like some RAW guidance on this please. But, if not explicitly available, then a response with lived experience of a GM on a similar ruling to do with resolving oder of events.

vampire the masquerade – What happens if a character’s declared action becomes impossible?

What happens if a character’s declared action becomes impossible before they can attempt it in the attack phase? Do the core rules support the idea that they get to pick a different action, or perform a similar action, or do they effectively lose the ability to act in that round?

For example, if a character wants to shoot someone but the target suddenly disappears from this plane of existence, is that character still forced to spend her round shooting at nothing, or can she now opt not to pull the trigger?

Since “shooting at the location where the target recently was” isn’t impossible, a better example might be if a character is disarmed before they can use a weapon. Can that character do nothing but follow through with their declared weapon-attack, albeit pantomimed?

Considering actions other than attacks, if someone declares that they’ll run across a room and through an open door, but the door is closed and bolted shut before their turn in the initiative order, are they then forced to run up to the door, or would they be allowed to remain in place since their intention is now impossible?

Notes

  • This is setting aside the rules for aborting an attack in favor of a defensive action.
  • It makes sense that changing an attack’s target during the attack phase would not be allowed, since that would give the attacker an unfair advantage in surprising a higher-initiative target who did not anticipate being attacked and thus had no defensive action prepared.

starfinder – Does the use of a gunner major action always preclude the use of the Snap Shot minor crew action?

In Starfinder, during starship combat, the Snap Shot minor crew action allows a crew member who has taken a major crew action earlier in the round to fire a starship weapon during the gunnery phase. The rules state:

You can fire one of your starship’s weapons with a –2 penalty to the gunnery check. You can take this action only if no other gunner actions have been taken during the gunnery phase (including snap shot).

The wording of the second sentence raises questions. Does it disallow Snap Shot actions completely if another character intends to take a gunner major action? Does it disallow Snap Shot actions unless they’re taken before all gunner major actions for the round? Or does it simply disallow Snap Shot if the character attempting it has already carried out a gunner major action?

The scenario I am facing in play is this: a pilot has completed a pilot major action in the Helm phase and positioned the ship to put the enemy ship in the port quadrant. There are two gunners on board. The first gunner has fired at the enemy ship with a turreted weapon. The second gunner has fired at the enemy ship with a port arc weapon. The pilot’s player points out that the ship also has a forward arc weapon that has the broad arc property–meaning that it can target ships in the port or starboard arcs with a -2 penalty. He wishes to Snap Shoot the broad arc weapon at the ship in the port arc with a cumulative penalty of -4 (-2 for firing outside the weapon’s normal arc and -2 for the fact that it is a Snap Shot). This seems like a reasonable request to me, but do the rules preclude it? If they do, then had the pilot declared this intention before the other gunners rolled, would he have been able to do it within the rules?

dnd 5e – Does a clay golem’s haste action actually give it more attacks?

A clay golem has an action called Haste that is thematically similar to the spell of the same name but mechanically rather different:

Haste (Recharge 5–6). Until the end of its next turn, the golem magically gains a +2 bonus to its AC, has advantage on Dexterity saving throws, and can use its slam attack as a bonus action.

At first glance, this appears to grant the golem one additional attack (as a bonus action). However, using the ability costs the golem its action, with which it could otherwise make 2 slam attacks. Since the ability lasts until the end of the golem’s next turn, it can attack with its bonus action on both the turn it uses the ability and the following turn, yielding a total of… 2 additional attacks. Thus, it seems that over the course of these 2 turns, the golem will get 4 attacks, regardless of whether it uses its Haste ability or not. The only difference is that with Haste, one of those attacks comes 1 turn later.

So, am I correct in finding that the net effect of the golem’s Haste action is to delay one of its attacks by one turn in return for improved defenses for 1 round, as opposed to actually granting additional attacks? Obviously there are cases where this is unambiguously a benefit, e.g. when the golem can’t get into melee on the current turn, but I suppose I find it a bit surprising that, if anything, the golem’s Haste action causes it to attack more slowly.

shortcut – How to set several triggers for the same action

I am someone that is pretty forgetful and don’t have the tendency to remember exact sentences.

This leads to me having every time I want to set an automation having to see what’s the name and then just clicking it.

I would like to set several sentences as the triggers for Shortcut actions so that I can associate more generic things to the correct action.

Example:

I want to preheat the car.

- "Hey Siri, preheat the car."
- "Hey Siri, warmup the car."
- "Hey Siri, I'm going to drive."

They are all the same to me. So could I define several things as a trigger for Siri? Or the only input is exactly what you type in the name of the shortcut action?

dnd 3.5e – Does Discipline Focus (Insightful Strikes) add the Wisdom bonus to each attack of Flashing Sun’s full-attack action?

Discipline Focus (Insightful Strikes) states the following:

At 4th level, you can add your Wisdom modifier as a bonus on damage
rolls whenever you execute a strike from the chosen discipline. At
12th level, you can choose a second discipline to which this ability
applies.

and Flashing Sun states the following:

Flashing sun allows you to make an additional melee attack during this
round. As part of this maneuver, you take a full attack action and
make your normal melee attacks. However, you can make one additional
attack this round at your highest attack bonus. All the attacks you
make this round, including the extra attack granted by this maneuver,
are made with a -2 penalty.

So, the thing is, Flashing Sun includes a full attack in its description, and Insightful Strikes says “damage rolls”, in plural. Does this mean that it adds the Wis bonus to each attack’s damage roll, only to the one added by the strike itself, or neither?

dnd 5e – If you cast a spell as a bonus action, can you use an action provided by some ongoing spells on the same turn?

If you cast a spell with a bonus action, you can’t cast a spell with a casting time of one action (PHB, p. 202):

A spell cast with a bonus action is especially swift. You must use a bonus action on your turn to cast the spell, provided that you haven’t already taken a bonus action this turn. You can’t cast another spell during the same turn, except for a cantrip with a casting time of 1 action

Does this apply to ongoing spells that provide an action after being cast?

Sunbeam

A beam of brilliant light flashes out from your hand in a 5-foot-wide, 60-foot-long line. Each creature in the line must make a Constitution saving throw. On a failed save, a creature takes 6d8 radiant damage and is blinded until your next turn. On a successful save, it takes half as much damage and isn’t blinded by this spell. Undead and oozes have disadvantage on this saving throw.

You can create a new line of radiance as your action on any turn until the spell ends.

For the duration, a mote of brilliant radiance shines in your hand. It sheds bright light in a 30-foot radius and dim light for an additional 30 feet. This light is sunlight.

Witch Bolt

A beam of crackling, blue energy lances out toward a creature within range, forming a sustained arc of lightning between you and the target. Make a ranged spell attack against that creature. On a hit, the target takes 1d12 lightning damage, and on each of your turns for the duration, you can use your action to deal 1d12 lightning damage to the target automatically

Am I wrong an interpreting this as allowing to cast a spell as a bonus action on the same turn as the actions provided by these spells?

  • Turn 1: I cast sunbeam
  • Turn 2: I cast hunter’s mark, then use the action provided by sunbeam to create a new beam.