Timeline for Frobenius formula
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 11, 2019 at 20:47 | comment | added | Gabriel | @RichardStanley In the last week I tried to understand what you said but without sucess. If it is not too troublesome for you, it would help me a lot to have a complete explanation. | |
| Feb 26, 2019 at 20:28 | comment | added | Richard Stanley | @GabrielRibeiro this should be in any introductory text on representations of finite groups, but I don't have access to this at the moment. One online reference is Proposition 3.7 of staff.fnwi.uva.nl/j.v.stokman/Aanvulling2.pdf. | |
| Feb 26, 2019 at 17:29 | comment | added | Gabriel | @RichardStanley could you explain in more details what you said in "The character values are the coefficients when the class sums are expanded in terms of these idempotents" ? I am in my first representation theory course so I don't have much background in it. | |
| Feb 25, 2019 at 0:23 | comment | added | Richard Stanley | For any finite group $G$, the numbers $N(G;C_1,C_2,C_3)$ tell us how to multiply conjugacy classes (that is, the sum of the elements of a conjugacy class) in the center of the group algebra $\mathbb{Z}[G]$. There is a unique set (up to sign and order) of primitive orthogonal idempotents in the center of the group algebra over $\mathbb{Z}$. The character values are the coefficients when the class sums are expanded in terms of these idempotents. (The sign is determined by the positivity of the character on the identity element of $G$.) In fact, this is how one proves Frobenius' formula. | |
| Feb 24, 2019 at 23:11 | history | edited | YCor |
edited tags; edited tags
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| Feb 24, 2019 at 20:54 | history | edited | Michael Hardy | CC BY-SA 4.0 |
added 9 characters in body
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| Feb 23, 2019 at 22:24 | comment | added | Fedor Petrov | Usually the first formula for the symmetric group is, viceversa, used for obtaining some information about products of conjugacy classes (and for characters some other formulae are used.) | |
| Feb 23, 2019 at 18:35 | review | First posts | |||
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| Feb 23, 2019 at 18:34 | history | asked | Gabriel | CC BY-SA 4.0 |