Timeline for Why we need to study representations of matrix groups?
Current License: CC BY-SA 3.0
20 events
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| S Dec 15, 2020 at 20:31 | history | edited | LSpice | CC BY-SA 4.0 |
Anonymous included extra tags; LSpice added `\operatorname`
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| S Dec 15, 2020 at 20:31 | history | suggested | CommunityBot |
I included extra tags.
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| Dec 15, 2020 at 19:28 | review | Suggested edits | |||
| S Dec 15, 2020 at 20:31 | |||||
| Dec 15, 2020 at 18:04 | answer | added | user122276 | timeline score: 1 | |
| Jan 22, 2014 at 8:33 | comment | added | Simon Pepin Lehalleur | @daril grinberg: a nice example is the study by Hausel, Rodriguez-Villegas of the topology of the character variety of GL_n(\mathbb{C}). See arxiv.org/abs/math/0612668 for the original paper and arxiv.org/abs/1102.1717 for a survey of recent developments. This is very much inspired by the (geometric) Langlands program, though, so maybe it doesn't count ! | |
| Jan 16, 2014 at 12:53 | comment | added | darij grinberg | I would definitely like to hear an answer to specifically the question where representations over $\mathbb C$ of matrix groups over $\mathbb F_q$ are used outside of algebraic number theory (which I'll probably never understand) and outside of the hunt for $\mathbb F_1$ (which is very nice but not an application in the strict sense of being useful in a proof). | |
| Jan 16, 2014 at 12:49 | comment | added | darij grinberg | It is nowadays commonly understood that texts about X are supposed to answer "how to X" and shouldn't waste space on questions like "why X" (after all, the reader obviously has a reason to X if he is reading a book about it!). In view of this, it might be useful to read something on a different subject -- the Langlands program perhaps, in this particular case? | |
| Jan 8, 2014 at 8:43 | answer | added | asv | timeline score: 9 | |
| Jan 6, 2014 at 23:44 | answer | added | paul garrett | timeline score: 14 | |
| Jan 6, 2014 at 21:43 | comment | added | Andy Putman | @AlainValette : As you say, sadly it often isn't... | |
| Jan 6, 2014 at 21:20 | comment | added | Alain Valette | @Andy: I agree that the question produced some good answers. On the other hand, this basic question should be answered in any introductory book in representation theory (even if it is not always so, unfortunately...) | |
| Jan 6, 2014 at 19:56 | comment | added | Andy Putman | @AlainValette : While I agree that it is borderline, the question has produced some very nice answers, so I vote to keep it open. | |
| Jan 6, 2014 at 18:47 | answer | added | John Wiltshire-Gordon | timeline score: 53 | |
| Jan 6, 2014 at 18:43 | answer | added | Ryan Reich | timeline score: 35 | |
| Jan 6, 2014 at 17:55 | review | Close votes | |||
| Jan 6, 2014 at 21:40 | |||||
| Jan 6, 2014 at 17:40 | comment | added | Alain Valette | This would be a good question for MathStackExchange. | |
| Jan 6, 2014 at 16:19 | comment | added | user76758 | Just as an aside, when I first began to learn about representation theory as an undergraduate, I had the exact same question as you raise above. Eventually I came to realize that the process of learning a subject via the "abstract" approach rather than through the natural examples that motivate it (and must have been in the back of the mind of the instructor without ever being discussed in the course) often leads to the wrong impression by a beginner as to what the point of a given mathematical theory is. | |
| Jan 6, 2014 at 16:10 | answer | added | Jim Humphreys | timeline score: 16 | |
| Jan 6, 2014 at 15:35 | comment | added | user76758 | A large purpose of representation theory is to use "symmetry" of objects arising in algebra, geometry, and analysis to better understand the structure of those objects; the aim is not to describe a group via matrices as an end unto itself. By the classification of finite simple groups, the most important finite groups are largely matrix groups over finite fields. If you study representations of a finite group $G$ in char. 0 and $G$ has a composition series whose successive quotients are matrix groups over finite fields then those matrices have nothing to do with ones in char. 0. | |
| Jan 6, 2014 at 14:41 | history | asked | Jianrong Li | CC BY-SA 3.0 |