A+ ... cannot emphasize the importance of what you accomplish with these lively and honest and yet rigorous videos. In the case of Representation theory, beginning example was inspiring and of course known to my person since I program those geometries day in and day out, but refreshing how you framed the bird's-eye view of the Representation Theory as such. If high school teachers accordingly taught the Representation concept , of course for simpler objects, we would have found far larger theoretical talent pool than available today. And actually new talents currently missing ...
Excited to see representations categorified, I remember reading somewhere that Frobenius reciprocity is an example of adjoint functors 50 years before Kan defined them!
It is even better ;-) Induction and restriction (the functors appearing in the abstract formulation of Frobenius reciprocity) are biadjoint, so left and right adjoints at the same time. That is so awesome. By the way: As far as I recall, Kan defined adjoint functors to abstractly model, among other things, Frobenius reciprocity. What you write sounds a bit backwards.
@@VisualMath The right adjoint of restriciton is coinduction: Coind_H^G := Hom_{kH}(kG, M) with the action g.f(x) := f(xg). If the index of H in G is finite, then we do have a natural isomorphism between Ind_H^G and Coind_H^G, but this is not true in general because the component maps include a sum indexed by a transversal of H in G.
@@JakubWaniek Thanks, that is right! But Frobenius reciprocity usually refers to finite groups. As you point out, then the difference can be ignored. Let us keep it simple ;-)
I am flattered, thanks! More importantly, your are happy, that is great. Now we just need to figure out whether there is indeed a bias towards German math RUclips channels ;-)
Oh, thank you so much! But whether this channel deserves more subscriptions is very questionable. Left aside the poor quality of my videos (ahh, needs to be improved), I think an abstract math channel is a just very niche type of channel ;-) Well, I like abstract math and I guess you do as well. So I personally do not care whether its rather exotic to be into some abstract nonsense such as e.g. representation theory ;-)
Awesome, I hope you will like the RT series. Or, to be more precise, I hope you like RT! RT is so beautiful and powerful at the same time - one of my favorites. (It is of course not important whether you like my videos ;-) But rather whether you will enjoy RT. If the videos are helpful, then that would be awesome, but its not required ;-))
@@VisualMath I actually work in RT (VOAs and Infinite Dimensional Lie Algebras), but I love seeing different perspectives on the subject from other mathematicians. It is an absolutely beautiful subject!
@@mathilike9460 Awesome! This series is mostly about finite groups and finite monoids. Well, that is not so far away, right? Use monstrous moonshine and you already have some VOA around ;-)
My intention is to give some answer to the question “What is...representation theory?”. Whether I was successful is very debatable ;-) and you should decide for yourself.
@@Epidemeus Everything is good: I understood the joke, but my answer was probably too silly. Anyway, thank you for your feedback, that is very much appriciated.
A+ ... cannot emphasize the importance of what you accomplish with these lively and honest and yet rigorous videos. In the case of Representation theory, beginning example was inspiring and of course known to my person since I program those geometries day in and day out, but refreshing how you framed the bird's-eye view of the Representation Theory as such.
If high school teachers accordingly taught the Representation concept , of course for simpler objects, we would have found far larger theoretical talent pool than available today. And actually new talents currently missing ...
You are always way to kind: I certainly do not deserve an A+. In any case, glad that you liked the video.
Excited to see representations categorified, I remember reading somewhere that Frobenius reciprocity is an example of adjoint functors 50 years before Kan defined them!
It is even better ;-) Induction and restriction (the functors appearing in the abstract formulation of Frobenius reciprocity) are biadjoint, so left and right adjoints at the same time. That is so awesome.
By the way: As far as I recall, Kan defined adjoint functors to abstractly model, among other things, Frobenius reciprocity. What you write sounds a bit backwards.
@@VisualMath The right adjoint of restriciton is coinduction: Coind_H^G := Hom_{kH}(kG, M) with the action g.f(x) := f(xg). If the index of H in G is finite, then we do have a natural isomorphism between Ind_H^G and Coind_H^G, but this is not true in general because the component maps include a sum indexed by a transversal of H in G.
@@JakubWaniek Thanks, that is right! But Frobenius reciprocity usually refers to finite groups. As you point out, then the difference can be ignored. Let us keep it simple ;-)
I discovered your channel yesterday and really enjoy your videos and your funny art
I personally wouldn't call it art ;-) But thanks for your very kind feedback anyway!
so many awesome math channels from germany! including yours! im glad :D
I am flattered, thanks! More importantly, your are happy, that is great. Now we just need to figure out whether there is indeed a bias towards German math RUclips channels ;-)
Thank you very much for this lecture series!
Thanks, I hope you will enjoy RT 😀
This channel really needs more subscribers. So great.
Oh, thank you so much!
But whether this channel deserves more subscriptions is very questionable. Left aside the poor quality of my videos (ahh, needs to be improved), I think an abstract math channel is a just very niche type of channel ;-)
Well, I like abstract math and I guess you do as well. So I personally do not care whether its rather exotic to be into some abstract nonsense such as e.g. representation theory ;-)
I couldn't agree more!
Just stumbled into your channel today. Very nice video. Looking forward to more in this series!
Awesome, I hope you will like the RT series. Or, to be more precise, I hope you like RT! RT is so beautiful and powerful at the same time - one of my favorites.
(It is of course not important whether you like my videos ;-) But rather whether you will enjoy RT. If the videos are helpful, then that would be awesome, but its not required ;-))
@@VisualMath I actually work in RT (VOAs and Infinite Dimensional Lie Algebras), but I love seeing different perspectives on the subject from other mathematicians. It is an absolutely beautiful subject!
@@mathilike9460 Awesome! This series is mostly about finite groups and finite monoids. Well, that is not so far away, right? Use monstrous moonshine and you already have some VOA around ;-)
Brilliant! Love your style
Wow, thank you for the nice words. It is good to know that my style is not completely off the tracks ;-)
Everyone keeps asking what is representation theory but never how its doing 😥
My intention is to give some answer to the question “What is...representation theory?”. Whether I was successful is very debatable ;-) and you should decide for yourself.
@@VisualMath thank you for your comment. I meant it as a joke, sorry for the misunderstanding. I think you did an excellent job!
@@Epidemeus Everything is good: I understood the joke, but my answer was probably too silly.
Anyway, thank you for your feedback, that is very much appriciated.
Hi
Thanks for saying Hi, you are welcome 😀
How many people come for movie download website on this video 😂😂
Well, who understands the RUclips/google or any other search/link algorithm ;-)
Great video, thank you.
Seems like you are in RT now - enjoy!
And as usual - thanks for the feedback!