Return of the Jedi question?

yes ,they are the emperor's hand [or the imperial guard]

they represent the dark side of the force

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The two in red are Imperial Guards. They initially started out in blue and were guards for Supreme Chancellor Palpatine but after he became deformed and declared himself emporer, the guards uniforms were changed to include the color. The Emporer's Hand was one specific anonymous person who was like an apprentice but was known only to the Emporer and operated in the shadows. One of the first was a girl named Mara Jade.

Are you talking about the guys in the red uniforms who look really cool? They're the Imperial Guard.

Personally, I don't follow what's in the books since that's not part of the original Star Wars universe, so I think of them simply as the Imperial Guard.

Those red cloaked guards are the Imperial Guard; a specially cloned guard for Palpatine with an affinity for the dark side of the force.

They are the Imperial Guard, also referred to as the Emperor's Hands. They are the Emperor's most trusted servants, and do his bidding in all manner of services.

They are infact the emporer's hand.

The old people in the "preist-like clothes" (purple-ish/blue robes and funny hats) are Imperial Advisors, they help Palpatine with the beauracratic details of running the Empire. They are NOT "Emporer's Hands" or warriors of any type. They are the highest level of number crunching, pencil-pushing beauracratic adminitrators, that's all.

The two in red robes and helmets are Imperial Royal Guards, based on the blue-robed and blue-helmed Republican Royal Guards that appear in the prequels near Chancellor Valorum in Epidsode 1 and Palpatine in Episode 2 and by the time of the Clone Wars (Episode 3) they adopted the red outfits that are seen in Return of the Jedi. The Royal Guards are highly trained warriors and are organized into various ranks and subgroups. There are Force-Sensitive Royal Guards that make up the most elite of their members and they do recieve some basic Force training, but they are NOT "Emporer's Hands" and are not trained in lightsaber combat.

There are NO "Emperor's Hands" shown in the films.

The first mention of these individuals appears in the Timothy Zahn Trilogy of novels, the character Mara Jade was an Emperor's Hand during the Rebellion Era and was forced to go into hiding after the Empire was defeated at Endor and began to crumble as the New Republic took power. Palpatine made her believe that she was his special student, his "Emperor's Hand" that would be entrusted with special assignments to maintain the loyalty and safety of the Empire.

The "Emperor's Hands" were a group of Force-Sensitve individuals that Palpatine personally trained in secret (Vader didn't even know about them) and each learned how to use the Force and wield lightsabers. By Sith tradition there could only be 2 Sith Lords at any given time (Palpatine & Vader until the end of ROTJ), but Palpatine still trained others in secret (like his Emperor's Hands and Imperial Inquisitors) so that he could replace Vader if he needed to. Palpatine does this secret planning against all his previous Sith Lords, he was grooming Dooku to become a Sith Lord in case he needed to replace Maul, he was grooming Anakin to replace Dooku, and he groomed Luke (once his found out who he was) to replace Vader, but before discovering Luke Skywalker's existence he was training others.

Each Emperor's Hand thought they were the only one, they knew nothing about other students being trained by Palpatine, except for Vader. They were trained to use their abilities as secret assassins and sabotours against what ever target Palpatine assigned them. Their identities were kept secret because of this, no one, except Palpatine, knew that these individuals existed. Palpatine would only meet with them in secret, and he would NEVER meet where Vader was present. Vader would be able to sense their strong Force abilities and either make plans of his own to kill the Emperor's Hand or (like he tried with Luke in ESB) attempt to bring them to his side so that he could use them to help kill Palpatine.

The first established Emperor's Hand, Mara Jade, was assigned to kill Luke Sykwalker, because Palpatine discovered Vader's attempt to turn Luke (in ESB) so that they could kill him and Vader could take over the Empire himself. Mara had disquised herself as a dancer performing in Jabba's Palace (she is not show in the film), her closest chance to get at Luke was to get on the Sailing Barge and make sure he dies at the Sarlacc Pit, but was left behind on Jabba's orders. Luke even has a dream of being back on Tatooine above the Sarlacc, but when R2 launches his lightsaber it changes course in mid-air and flies into the hand of a shadowy female outline on Jabba's Sailing Barge... but he never sees her face.

I haven't read any novels with other Emperor's Hands (but I've heard they appear in other book) and the only one I know about is Mara Jade.

if they are in red, i think they are the official Imperial Gaurd, that is all i know