Irreducible representations (irreps) | Representation theory episode 3

[@LunizIsGlacey]

Amazing video!! A really great introduction to some core ideas in representation theory :)

[@AllAnglesMath]

Thank you!

[@DeathSugar]

Also please don't gradient plane points (like 6:18). Group coloring doesn't look like turns into gradient.

[@authenticallysuperficial9874]

Very cool!

[@DeathSugar]

Are we gonna study whole table of groups including sporadic ones?

[@AllAnglesMath]

We won't be listing all of the groups. I may however make a video about the monster group later, the biggest of the sporadic groups.

[@DeathSugar]

@@AllAnglesMath nah, there's many videos about monster, moonshine etc. I would prefer if the idea behind sporadic/non-sporadic were clarified and the way they are generated.

[@Grateful92]

Wow!

[@DeathSugar]

Does more dimension will yield bigger sign group? like with 3D space which has 4 diagonals it become sign group of that size?

[@TheOneMaddin]

The sign representation is always 1-dimensional.

[@DeathSugar]

@@TheOneMaddin 1 dimensional how? it's at least 1x2 in the video. Will it become 1xn for any n dimension square?

[@DeathSugar]

On the other hand depends on what object of symmetry chosen. For a cube it will form cyclic group of size 6 (if i counted correctly) - C6 which composed of C2xC3, so I guess it's also be the case for it's sign and others. which is if I counted correctly and it's underlying structure definitely composite.

[@TheOneMaddin]

@@DeathSugar Sorry, I don't have the time to recall the definitions, but if you use the correct definition of sign representaion, it is ALWAYS 1D. If you mean something different then my answer might not apply but then I also don't know what you are asking.

[@DeathSugar]

@@TheOneMaddinspatial 1D is literally dot on the numberline. 1D matrix is 1x1. sign matrix used in video is 1x2 so it's by definition cannot be 1D. when you use higher dimension group it has more freedom dimensions so it either stays the same or start extend to things like i -I j -j etc.

[@omipial2084]

4:12-;