Timeline for How to explicitly expand a class function in terms of irreducible characters?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Dec 21, 2017 at 18:37 | comment | added | Jim Humphreys | @Lior: Sorry for the long delay in responding to your comment. I had in mind some highly non-abelian (say simple) group, which would be a good test case. The point is that character tables are known explicitly for many small simple groups, permitting experimentation. | |
| Dec 18, 2017 at 3:04 | review | Close votes | |||
| Dec 18, 2017 at 10:31 | |||||
| Dec 13, 2017 at 16:32 | vote | accept | Lior Bary-Soroker | ||
| Dec 13, 2017 at 15:47 | answer | added | Benjamin Steinberg | timeline score: 4 | |
| Dec 13, 2017 at 9:50 | comment | added | Neil Strickland | Your $f$ can be written in terms of Adams operations as $f=n^{-1}\psi^d(\chi_1)$, so you might find it helpful to consider the relationship between Adams operations and exterior powers. | |
| Dec 13, 2017 at 9:26 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
deleted 9 characters in body
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| Dec 13, 2017 at 3:05 | comment | added | Lior Bary-Soroker | @IgorRivin It is; but I hoped to as nice formula for the Fourier coefficients of that particular function of order dividing d as we have in the abelian case. | |
| Dec 13, 2017 at 3:04 | comment | added | Igor Rivin | Isn't this just the Fourier transform? | |
| Dec 13, 2017 at 2:57 | comment | added | Lior Bary-Soroker | @JimHumphreys Well, the formula I wrote above carries on to abelian groups. I do not know what happens, say, in nilpotent. | |
| Dec 13, 2017 at 0:28 | review | Close votes | |||
| Dec 13, 2017 at 1:58 | |||||
| Dec 12, 2017 at 23:25 | comment | added | Jim Humphreys | @Lior: It does depend on what yiu mean by "explicit formula", but in any case I'm not optimistic about handling an arbitrary finite group. Are there more complicated examples than cyclic groups? | |
| Dec 12, 2017 at 22:43 | comment | added | Lior Bary-Soroker | @LSpice I don’t think so since I can’t evaluate it in general. | |
| Dec 12, 2017 at 22:36 | comment | added | Benjamin Steinberg | When d=2 this is related to the Frobenius-Schur indicator. | |
| Dec 12, 2017 at 22:26 | comment | added | LSpice | Haven't you given an explicit formula for $c_\chi$? | |
| Dec 12, 2017 at 22:18 | history | asked | Lior Bary-Soroker | CC BY-SA 3.0 |