Timeline for number of irreducible representations over general fields
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 3, 2010 at 11:50 | comment | added | Pete L. Clark | There is no need to do any of these tensor product tricks. For any field $k$ of characteristic $0$, the irreducible representations of a finite group $G$ are precisely the simple submodules of the semisimple group algebra $k[G]$, so are finite in number. Some of these irreducible representations may become reducible after extension (keyword: Schur index), but that's orthogonal to the question at hand. | |
| Jan 2, 2010 at 2:57 | comment | added | natura | thank you! but how does one deduce finiteness after tensoring with complex numbers? I mean, irreducible representations in Q_p can become reducible after tensoring with C, right? And what do you mean by working on WD representations? What are the results? Thank you! | |
| Jan 1, 2010 at 20:31 | comment | added | David Zureick-Brown | Small point: you can always embed a p-adic field into the complex numbers and deduce finiteness in this way. For infinite, profinite groups you usually require the representation to be continuous, so and the embedding of a p-adic field into the complex numbers isn't continuous; it still turns out to be a useful thing to do though in some case (e.g. Weil-Deligne representations). | |
| Jan 1, 2010 at 16:14 | answer | added | Mariano Suárez-Álvarez | timeline score: 5 | |
| Jan 1, 2010 at 12:16 | answer | added | Akhil Mathew | timeline score: 8 | |
| Jan 1, 2010 at 7:01 | history | asked | natura | CC BY-SA 2.5 |