Sergey Finsky
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 Sep24 awarded Autobiographer Jul2 awarded Curious May30 awarded Yearling Dec29 awarded Tumbleweed May14 awarded Caucus Mar21 comment Trying to prove that operator is compact Do you have any problems in understanding locally bounding criteria? Mar4 answered Trying to prove that operator is compact Mar1 awarded Teacher Mar1 answered Determinant of matrix exponential? Feb16 accepted Boolean ring. Representation as direct product? Feb16 comment Boolean ring. Representation as direct product? Thank you! Yes, the reason I tangled up is that I haven't notice that the proof of the theorem in the paper, I provided, was for general(infinite) case. Feb16 revised Boolean ring. Representation as direct product? Forgot to say that I am only interested in finite case. Feb16 comment Boolean ring. Representation as direct product? Sorry guys, I forgot to say that I am only interested in finite case. I will edit it now. Feb16 asked Boolean ring. Representation as direct product? Feb11 comment Asymptotics with prime of form 4k+3 Sorry for not responding for such a long time, I kept forgetting to respond that your answer solves original question, which can be easily deduced from standart $\delta - \epsilon$ arguments. Jan30 comment Induced representation, Ind(Res(U)) I will have a clear look on the 1st problem in tomorrow morning. For the second - sorry, I meant not $W$, but $Ind(W)$ and now we can form such sum, since we are trying to reconstruct $U$ from $\underline{G}$-module $U \otimes Ind(W)$ Jan30 comment Induced representation, Ind(Res(U)) For the 1st problem: (at first, just to be sure that I understood everything correctly, we need $H$-modules $\alpha$ and $\beta$, don't we?) and the problem is: what would happen if we wanted to send some element of the form $(x \otimes_H w) \otimes yu$, where $x^{-1}y \ne 1 mod H$, we would send it to $x \otimes (w \otimes_H x^{-1}yu$, but $H$ acts differently on $U$ and $x^{-1}yU$ in general case... That's seems to be a problem here. For the second part: let we consider $U \otimes (\sum_{g \in G} gx)$ for some $x \in W$, it seems that we can recover action of $G$ on $U$. Jan30 awarded Commentator Jan30 comment Induced representation, Ind(Res(U)) There are 2 issues: first is dealt with module map $\alpha$ : why it sends elements to $kG \otimes H(W \otimes U_{H})$, but not to $kG \otimes H(W \otimes U)$?And the second is a bit psychological: it doesn't seems that restriction serves the whole information about the original representation. (apart from the $U_{H}$ I do understand everything from the proof, but psychologically I can't admit it, because there are many representations, restrictions of which collides (there are trivial and alternating representations of $Sym($n$)$, restrictions to $A_n$ of which equal),despite the formula. Jan30 asked Induced representation, Ind(Res(U))