Timeline for Infinite dimensional unitary representations of SU(2) for non-half-integer j?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2010 at 7:27 | answer | added | Victor Protsak | timeline score: 4 | |
| Jun 12, 2010 at 4:46 | comment | added | S. Carnahan♦ | Oops, the continuous parameter comes from the noncompact part of the torus, which doesn't really intersect SU(2) much. Sorry about the mistake. | |
| Jun 11, 2010 at 21:59 | vote | accept | Daniel | ||
| Jun 11, 2010 at 20:48 | answer | added | B R | timeline score: 11 | |
| Jun 11, 2010 at 19:57 | comment | added | Daniel | I've just checked now and actually if the principal series of $SL_2(C)$ is labelled by $(\nu,\rho)$ where $\nu$ is half-integer, $\rho$ is continuous, then if it is restricted to $SU(2)$ it will decompose into an infinite sum of representations with $j = \nu, \nu+1, \nu+2, ....$: $(\nu,\rho) = \sum_{j=\nu}^{\infty} j$ So we do not get infinite dimensional unitary irreducible representations of $SU(2)$ this way. | |
| Jun 11, 2010 at 19:26 | comment | added | S. Carnahan♦ | You can restrict principal series representations of $SL_2(\mathbb{C})$ to $SU(2)$. They have a continuous parameter, and they are unitary. | |
| Jun 11, 2010 at 19:14 | history | asked | Daniel | CC BY-SA 2.5 |