If the characters of two representations are equal, what additional information do we need to conclude they’re isomorphic?

Let $ (\pi,V)$ be a finite dimensional complex representation of a group $ G$ . If $ G$ is finite, then $ \pi$ is determined up to isomorphism by its character $ \chi_{\pi}$ .

What about the case where $ G$ is not necessarily finite? I doubt it’s still true that $ \pi$ is determined by its character, even up to semisimplification.

If $ \pi_1, \pi_2$ are two semisimple representations of $ G$ with the same character, what other properties would $ \pi_1$ and $ \pi_2$ have to share to conclude they are isomorphic? For example, suppose $ H$ is a subgroup of finite index of $ G$ , and we have not only $ \chi_{\pi_1} = \chi_{\pi_2}$ , but also $ \pi_1|H \cong \pi_2|H$ .

The reason I’m asking is I have a semisimple representation $ \pi$ of a group $ G$ which I believe is isomorphic to some induced representation $ \operatorname{Ind}_H^G \sigma$ for a semisimple representation $ \sigma$ of $ H$ . I know how to directly construct an isomorphism between these guys, but it’s very tedious. But it’s easy for me to show that their characters are equal and that their restrictions to $ H$ are isomorphic.

Does the “Pierce Magical Concealment” feat allow a character to see magically concealed characters?

One of the players of the oneshot campaign that I’m writing chose the feat Pierce Magical Concealment (Complete Arcane, p.81), as a DM I’m not sure how it would work in an encounter I am planning.

The manual states about the Pierce Magical Concealment feat:

You ignore the miss chance provided by certain magical effects.

Your fierce contempt for magic allows you to disregard the miss chance granted by spells or spell-like abilities such as darkness, blur, invisibility, obscuring mist, ghostform (see page 109), and spells when used to create concealment effects (such as a wizard using permanent image to fill a corridor with illusory fire and smoke). In addition, when facing a creature protected by mirror image, you can immediately pick out the real creature from its figments. Your ability to ignore the miss chance granted by magical concealment doesn’t grant you any ability to ignore nonmagical concealment (so you would still have a 20% miss chance against an invisible creature hiding in fog, for example).

This doesn’t specify if a character with this feat can actually see an enemy that is, for example, under the effect of the spell Invisibility (Player’s Handbook, p. 245).

I am planning an encounter in which the party will be invited by a wizard for dinner, an assassin under the effect of invisibility will pretend to be an Unseen Servant (Player’s Handbook, p. 297) until the wizard gives him the signal to attack the party.

Will the character that has the Pierce Magical Concealment feat be able to see the assassin, or at least have any advantage in noticing he is not an Unseen Servant?

How do I get player characters who have non-adventurer backstories to go on adventures?

I have had an annoying issue where all my players make characters that don’t adventure and have jobs! This makes it really hard to incorporate them into the story and gives them very little backstory (as they want to never have met the rest of the party).

How do I get the players to stop this and go adventuring?

Characters Converted to HTML Entities in Submission Email?

I have a webform in which I’ve developed a custom module to add a value to a hidden element based on inputs received by the person submitting the form. I also have an email handler specified that sends the submitted values, including the value assigned to the hidden field, to me as the site administrator. I’m using the Swift Mailer to get uploaded files delivered as email attachments. I have the email configured to be sent as plain text.

This all seems to be working fine, with the exception that quote characters (“) that my module adds to the value of my hidden field and other characters that were typed into a text field are being converted by something into HTML entities ("). I’ve checked the value of the fields via debug logging and things look fine when the field values is saved. What might be converting the quote characters, and what can I do to avoid the conversion?

How to match a string with regex where specific character appears at least once so that the first neighbours characters are different from it?

I’m searching for the shortest regex that can matches a string described in a question. I’m also interested in solution where regex matches string where specific character never appears surounded with same character.

This is currently my solution (in this case specific charcter is g):

^.*[^g]{1}g[^g]{1}.*$  |^g[^g]{1}.*$  |^.*[^g]{1}g$  |^g$  " 

I expect that regex matches strings like:aaagaa, g, gdddg, agaagga ,but doesn’t matches: aaagg,ggaagg,gg, ggg.

Special characters in email body

I’m attempting to send an email from a Drupal 8 module I’m developing, and it works except that special characters (‘ < >) seem to be getting escaped.

My module has a configuration to select whether the emails are plain text or HTML (using Swiftmailer). In plain text messages, apostrophies get replaced by ' while in the html messages, all HTML tags receive similar treatment, so the message arrives, but the HTML tags are all shown in the message, rather than formatting it.

Heres an extract from my hook_mail handler:

  $  message['subject'] = $  params['subject'];   $  body = $  params['body'];   if ($  config->get('confirmation.format_html')) {     // Set up HTML email.     $  message['headers']['Content-Type'] = 'text/html; charset=UTF-8';     $  message['body'][] = $  body;  // HTML version of message body.     $  message['plain'] = \Drupal\Component\Utility\SafeMarkup::checkPlain($  params['body']);  // Plain text version of body.   } else {     $  message['body'][] = $  params['body'];  // Plain text version of body.   } 

It seems there’s some escapement of special HTML characters going on, but I can’t see where.

Any help greatly appreciated.

James

rsync verbose print folders with strange characters

Using rsync -avh the list of folders stops printing when getting to a directory ls calls ''$ '20''퓬ƒTƒ“ƒvƒ‹' (badly encoded Japanese text that doesn’t appear to be EUC-JP, ISO-2022-JP, or SHIFT_JIS). However it seems like rsync continues transferring, just not displaying. How can I get rsync to continue printing information?

What are the options for player characters to create traps?

The ranger and rogue in my game were asking about setting traps in preparation for a battle that was coming. Another player is convinced rogues can make traps because he saw it happen in D&D sessions online (in streams). But the only information about making traps that I can find seems to be addressed at DMs, in the context of designing dungeons and such.

Research

Rogues do get proficiency in Thieves’ tools, but this only lets you disarm traps (not create them):

This set of tools includes a small file, a set of lock picks, a small mirror mounted on a metal handle, a set of narrow-bladed scissors, and a pair of pliers. Proficiency with these tools lets you add your proficiency bonus to any ability checks you make to disarm traps or open locks.

PCs are also able to buy Hunting Traps. So it would make sense that nifty rogues could backwards-engineer traps that they can buy and/or disarm, but I’m curious whether the books cover guidance in this regard.

Related:

  • What options exist for player-controlled traps? (only covers the use of spells)
  • Unearthed Arcana: Traps Revisited

Question

What are the options for player characters to create traps?

By ‘traps’ I mean methods or mechanisms designed to influence, hinder, or expose enemies, which must be set up before use, operate on a trigger (set off by target or by trapper are both fine). For this question I’m excluding spells that function as traps.

gpg –armor –export-secret-key differ on last 4 characters

I created a backup of a gpg key by doing:

gpg -a --export-secret-keys foo@bar > private.key gpg -a --export foo@bar > public.key 

Then on another system, I import them:

gpg --import private.key gpg --import public.key 

I trusted the key as ultimate, and the backup seems to be working, the only thing that I notice is that when doing:

gpg --armor --export-secret-key foo@bar 

The last 4 characters differ for example:

dutrV4c4hoPc6ntI3n9VztsL4LmmvoCcH969nJD6bTh4H1VMH98r8zECshtCSfVE tMIIhXjA9xO1IZ6vMqHJU8TNhV2ttOE1Z/sUjcB46X4= =TGyi -----END PGP PRIVATE KEY BLOCK----- 

In the new computer:

dutrV4c4hoPc6ntI3n9VztsL4LmmvoCcH969nJD6bTh4H1VMH98r8zECshtCSfVE tMIIhXjA9xO1IZ6vMqHJU8TNhV2ttOE1Z/sUjcB46X4= =/eDz -----END PGP PRIVATE KEY BLOCK----- 

Wondering why the last characters differ, in this case =TGyi and =/eDz