Timeline for Peter–Weyl decomposition for compact Lie groups with isomorphic Lie algebras
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 22, 2020 at 22:50 | comment | added | Qiaochu Yuan | @Piet: yes, that's right (for finite-dimensional representations). | |
| Dec 22, 2020 at 22:19 | comment | added | LSpice | @PietBongers, assuming that $\pi(G)$ means $\pi_1(G)$, then this is so; Wikipedia calls it the homomorphisms theorem, although I am not sure if this terminology is standard. | |
| Dec 22, 2020 at 21:00 | comment | added | Piet Bongers | @QiaochuYuan: Thanks a lot for the extra comments. So if I have understood correctly, for a Lie group $G$, will the irreps of $G$ coincide with the irreps of $\frak{g}$ when $\pi(G)$ is trivial? | |
| Dec 22, 2020 at 20:06 | history | edited | Qiaochu Yuan | CC BY-SA 4.0 |
added 853 characters in body
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| Dec 22, 2020 at 20:06 | vote | accept | Piet Bongers | ||
| Dec 22, 2020 at 20:03 | comment | added | Qiaochu Yuan | @Piet: it's exactly as LSpice says, you get a double cover so again there are "twice" as many irreducibles. | |
| Dec 22, 2020 at 20:02 | comment | added | LSpice | @PietBongers, addressed in a comment on the main question (although maybe @QiaochuYuan will have more to say). | |
| Dec 22, 2020 at 19:57 | comment | added | Piet Bongers | So the example I am thinking about is $U_2$ and $SU_2 \times U_1$. Does $SU_2 \times U_1$ have more irreducible representations than $U_2$? | |
| Dec 22, 2020 at 19:53 | vote | accept | Piet Bongers | ||
| Dec 22, 2020 at 19:55 | |||||
| Dec 22, 2020 at 19:41 | history | answered | Qiaochu Yuan | CC BY-SA 4.0 |