Timeline for Vanishing of Clebsch–Gordan coefficients
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 4, 2021 at 13:37 | comment | added | Robert Bryant | Looking at this again, I realize that I should have specified that, in the case of $\mathrm{SU}(2)$, the weights $\lambda$, $\nu$, and $\mu$, etc. range over the nonnegative integers, while, in the case of $\mathrm{SO}(3)$, these weights range over the nonnegative even integers. Note that, in both cases, $\dim_\mathbb{C}V_\lambda = \lambda+1$, and, when $\lambda$ is even, $V_\lambda = \mathbb{C}\otimes W_\lambda$ where $W_\lambda$ is a real representation. | |
| Dec 23, 2020 at 1:41 | comment | added | shrinklemma | @Professor Bryant I see. I will try to analyze the Steinberg formula and look for their vanishing properties. The formula looks like some sort of alternating sum, so the question of vanishing seems interesting... | |
| Dec 22, 2020 at 10:29 | comment | added | Robert Bryant | Such question are answered by the Steinberg multiplicity formula (a consequence of the Weyl character formula). 'Clebsch-Gordan' usually means the results of this formula applied to either $\mathrm{SO}(3)$ or $\mathrm{SU}(2)$. There, the answer is relatively simple, since $$\pi_\lambda\otimes\pi_\mu \simeq \pi_{\lambda+\mu}\oplus \pi_{\lambda+\mu-2}\oplus \pi_{\lambda+\mu-4}\oplus\cdots\oplus\pi_{|\lambda-\mu|}$$ for $\lambda,\mu\ge0$. | |
| Dec 22, 2020 at 5:45 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Formula hyperlinking
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| Dec 22, 2020 at 4:51 | history | edited | shrinklemma | CC BY-SA 4.0 |
added 72 characters in body
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| Dec 22, 2020 at 4:43 | history | asked | shrinklemma | CC BY-SA 4.0 |