Timeline for Does $SU(2)\cong Sp(1)\subset SO(5)$ factor through $Spin(5)\cong Sp(2)$ as the standard embedding $Sp(1) \to Sp(2)$?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 9, 2018 at 20:48 | vote | accept | Wilhelm L. | ||
| Apr 9, 2018 at 19:36 | answer | added | Ben Webster♦ | timeline score: 5 | |
| Apr 9, 2018 at 19:15 | comment | added | YCor | Over the reals, the irreducibles of $SU(2)$ are $V_n$ of dimension $n$ for $n\ge 1$ odd (which factor through $SO(3)$) and $W_n$ for $n\ge 4$ mutliple of $4$, of dimension $4n$ and faithful. Therefore in dimension 5 there's a single faithful representation namely $W_4\oplus V_1$. I guess it's also unique (at least its image) up to conjugation in $SO(5)$. So probably the answer is yes iff the composite map $Sp(1)\to Sp(2)\to SO(5)$ (where the left-hand is the standard embedding) is injective. | |
| Apr 9, 2018 at 19:08 | history | asked | Wilhelm L. | CC BY-SA 3.0 |