Timeline for Induced representations of topological groups
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Dec 14, 2011 at 16:06 | vote | accept | Matthew Daws | ||
| Dec 14, 2011 at 8:37 | comment | added | Marc Palm | mathoverflow.net/questions/1534/… | |
| Dec 14, 2011 at 8:24 | comment | added | Matthew Daws | @Yemon: Yes, Induction is a left adjoint for Restriction; so Restriction is a right adjoint for Induction (I think I didn't commit myself as to which was which, as it were!) As for which modules, I already say "'hermitian module', i.e. unitary representations on Hilbert spaces"...?? | |
| Dec 14, 2011 at 8:06 | comment | added | Yemon Choi | Since I suspect (ahem) that you are primarily interested in unitary, or at least Banach, representations, perhaps you should add that to the question? | |
| Dec 14, 2011 at 7:56 | answer | added | Marc Palm | timeline score: 9 | |
| Dec 14, 2011 at 4:06 | answer | added | Jesse Peterson | timeline score: 10 | |
| Dec 13, 2011 at 23:52 | comment | added | Yemon Choi | I'm a bit confused, Matt: the isomorphism written in your question says that induction is left adjoint to restriction; the induced representation is the one "freely generated" by a given representation of $H$. The isomorphism in your comment would be saying that induction is right adjoint to restriction. | |
| Dec 13, 2011 at 20:28 | comment | added | Matthew Daws | @Benjamin: If I understand your comment, then I should have stressed right adjoint-- I think it's too much to hope that $\operatorname{Hom}_G(U,\operatorname{Ind}^G_H(V)) \cong \operatorname{Hom}_H(\operatorname{Res}(U),V)$ I think. So, yes, I agree! | |
| Dec 13, 2011 at 17:26 | comment | added | Benjamin Steinberg | I think induction in this setting is actually conduction with topological overtones, so it maybe right adjoint to restriction but I am no expert. | |
| Dec 13, 2011 at 14:31 | history | asked | Matthew Daws | CC BY-SA 3.0 |