Timeline for Bernstein's presentation for the Hecke algebra
Current License: CC BY-SA 4.0
8 events
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| Feb 3, 2022 at 17:29 | history | edited | Glorfindel | CC BY-SA 4.0 |
3 broken links fixed
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| Oct 1, 2010 at 9:19 | comment | added | Kevin McGerty | @Marty: I think if you look at Lusztig's second paper on unipotent representations of p-adic groups he discusses the unramified case, possibly quite tersely, but it might be worth a look. | |
| Sep 29, 2010 at 17:46 | comment | added | Jim Humphreys |
Yes, the affine Hecke algebra is not tied directly to a specific application though it was originally studied in the context of split $p$-adic groups (where the affine Weyl group can replace the finite Weyl group to give an interesting BN-pair structure in the algebraic group).
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| Sep 29, 2010 at 3:03 | comment | added | user2490 | Marty: Lusztig sets everything up to work in the non-split case. (Would you expect anything less?) He does not mention algebraic groups in the JAMS article, and so in order to connect his algebra to an algebraic group, you'd have to dig through Bruhat-Tits. For the unramified case, that digging is (as you probably know) not too painful. | |
| Sep 28, 2010 at 17:53 | comment | added | Jim Humphreys | Marty: The short answer is no. My knowledge of p-adic groups and such is fairly superficial. The older work of Iwahori-Matsumoto on "Hecke" algebras involved just split groups, but since then the subject has been developed (by a lot of people) far beyond my attention span. | |
| Sep 28, 2010 at 16:27 | comment | added | Marty | Do you know of a reference that treats the nonsplit case as well? Even the case of a quasisplit group that splits over an unramified extension (a so-called "unramified group" by some) would be helpful to me. | |
| Sep 28, 2010 at 15:52 | history | edited | Jim Humphreys | CC BY-SA 2.5 |
added 438 characters in body
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| Sep 28, 2010 at 15:23 | history | answered | Jim Humphreys | CC BY-SA 2.5 |