Timeline for Borel's Paris Lectures
Current License: CC BY-SA 3.0
9 events
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| Apr 29, 2013 at 17:12 | comment | added | admissiblecycle | @paul garrett Thanks a lot for the explanation, it makes a lot more sense now! :) | |
| Apr 29, 2013 at 15:12 | comment | added | paul garrett | I don't know an alternate reference, but I think 5.6 (that $z$-finite functions on a split component are exponential polynomials) should follow from the Harish-Chandra isomorphism (that the center of the enveloping algebra is identifiable with Weyl-group-symmetric elements of the enveloping algebra of $\mathfrak a$), and thus reducing to the rank-one case, which amounts to solving $P(y\cdot {d\over dy})u=0$ or $P({d\over dx})u=0$ after taking logarithms, where $P$ is a polynomial. Thus, this reduces to constant-coefficient ODEs on the real line. | |
| Apr 29, 2013 at 13:50 | history | edited | ACL | CC BY-SA 3.0 |
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| Apr 29, 2013 at 13:49 | comment | added | admissiblecycle | Thanks a lot for your comment. In Borel's Paris lecture notes, I was hoping to find a proof of Prop 5.6, page 23 of the Park City/IAS volume, as I don't quite follow Harish-Chandra's proof. Do you know where I can find an alternate proof of Prop 5.6? | |
| Apr 29, 2013 at 13:15 | vote | accept | admissiblecycle | ||
| Apr 29, 2013 at 13:02 | answer | added | Jim Humphreys | timeline score: 13 | |
| Apr 29, 2013 at 12:51 | comment | added | paul garrett | Some fragments of these occur in Borel's little book on SL(2,R), and in his Park City/IAS note, although the latter also partly refers to the original unpublished notes. The "theory of the constant term" arguments in the little book seem to scale up well. The general reduction theory is probably that in the Borel-HarishChandra book on arithmetic groups. But, no, I've never seen these notes. | |
| Apr 29, 2013 at 12:02 | history | edited | admissiblecycle |
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| Apr 29, 2013 at 11:43 | history | asked | admissiblecycle | CC BY-SA 3.0 |