Timeline for Is $\sum_{\rho \text{ irred. }} \deg(\rho) \chi_{\rho}(g)=0$ for every group element $1 \neq g \in G$ of the finite group $G$?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Dec 25, 2021 at 21:27 | comment | added | mathoverflowUser | @BenjaminSteinberg: thanks for the clarification | |
| Dec 25, 2021 at 20:48 | comment | added | Benjamin Steinberg | Now that you replaced deg^2 by deg this is just the standard statement that an irreducible representation appears with multiplicity equal to its degree in the regular representation and so your sum is computing the character of the regular representation which is 0 on all nonidentity elements and |G| on the identity | |
| Dec 25, 2021 at 19:52 | vote | accept | mathoverflowUser | ||
| Dec 25, 2021 at 19:52 | comment | added | mathoverflowUser | I am not sure I understand your answer. Can you please relate to the notation used in the question? | |
| Dec 25, 2021 at 15:37 | comment | added | Benjamin Steinberg | Since @GeoffRobinson's comment is no longer here it said the desired result is false for the symmetric group on 3 letters where g has order 3. | |
| Dec 25, 2021 at 14:45 | comment | added | Yemon Choi | In light of the error, I don't really think this counts as a "solution". This is a bit like saying "the value of six times nine is 42 (if you replace the nine by seven)" | |
| Dec 25, 2021 at 14:03 | comment | added | user130903 | I realised that and already edited my solution accordingly. | |
| Dec 25, 2021 at 14:02 | comment | added | Benjamin Steinberg | The regular character is the sum of $deg(\rho)\chi_{\rho}$ without the square. So what you want is true without the square but false with the square as @GeoffRobinson explained | |
| Dec 25, 2021 at 13:59 | history | edited | user130903 | CC BY-SA 4.0 |
added 72 characters in body
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| Dec 25, 2021 at 13:38 | comment | added | Tommaso Scognamiglio | I'm sorry but what do you mean by Plancherel theorem? | |
| Dec 25, 2021 at 12:37 | vote | accept | mathoverflowUser | ||
| Dec 25, 2021 at 13:50 | |||||
| Dec 25, 2021 at 12:37 | comment | added | mathoverflowUser | thanks for your insight | |
| Dec 25, 2021 at 12:34 | history | answered | user130903 | CC BY-SA 4.0 |