Timeline for Why is the cuspidal spectrum discrete?
Current License: CC BY-SA 3.0
7 events
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| Jul 16, 2011 at 16:23 | comment | added | paul garrett | The argument for discreteness of cuspforms in Lax-Phillips' "Scattering theory for automorphic forms", pp 204-6, is essentially independent of the rest of the book, and for $SL_2$ may give a more intuitive argument than the integral operators argument, athough not clearly suggesting the general case. | |
| Apr 11, 2011 at 8:36 | comment | added | GH from MO | I think it is not true that all the mess comes from a maximal unipotent subgroup. One needs to consider all parabolic subgroups containing a fixed minimal parabolic subgroup, define a correction kernel for each of them, and modify the original kernel with the sum of these. Then one needs to show that the modified operator is compact which boils down to a detailed understanding of the group and its parabolic subgroups. Admittedly, I am no expert in the general theory, but I don't know about a more conceptual proof. | |
| Apr 11, 2011 at 6:06 | comment | added | Marc Palm | I accept this as the answer, because it answers the question as stated above. But I was hoping something more conceptual. If you'd no glur how to achieve the spectral decomposition for $GL_2$, how do you come with integrating over $N$? Why is it reasonable for $GL_n$ to guess that all the mess comes from the induction from a maximal unipotent subgroup, i.e. from the smaller $GL_m, m<n$? | |
| Apr 11, 2011 at 5:55 | vote | accept | Marc Palm | ||
| Apr 10, 2011 at 18:24 | history | edited | GH from MO | CC BY-SA 3.0 |
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| Apr 10, 2011 at 16:28 | history | edited | GH from MO | CC BY-SA 3.0 |
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| Apr 10, 2011 at 16:09 | history | answered | GH from MO | CC BY-SA 3.0 |