Timeline for Hecke algebra of GL(2,F)
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 10, 2019 at 4:38 | comment | added | Will Sawin | @LSpice I think I was thinking about Bruhat decompositions for affine Lie groups, where Borels are compact, but I don't really know. | |
| Jun 10, 2019 at 3:14 | comment | added | LSpice | I think you mean the Iwahori or Cartan decomposition (depending on what your $K$ is), not the Bruhat decomposition (which corresponds to the non-compact choice of $K = B$ a Borel subgroup). | |
| Feb 21, 2018 at 4:19 | comment | added | Kostas Psaromiligkos | I understand now. Well I think I understand how the Satake transform works, but even using the Bernstein presentation immediately should give the result for both the whole algebra (without fixing a K) and the center (H(G,K)) right? Can you explain to me in this simple case how does the Bernstein presentation give $\mathbb{C}[z_1^{\pm},z_2^{\pm}]^{S_2}$? | |
| Feb 15, 2018 at 16:47 | vote | accept | Kostas Psaromiligkos | ||
| Feb 15, 2018 at 16:48 | |||||
| Feb 14, 2018 at 21:14 | comment | added | Will Sawin | @KostasPsaromiligkos It's the other way around, the usual Hecke algebra is commutative - it's given by what you wrote down with the Satake isomorphism - and the Iwahori-Hecke algebra is not. | |
| Feb 14, 2018 at 20:27 | comment | added | Kostas Psaromiligkos | As I said I probably have some misconceptions...The basic differencein what I've seen is that Iwahori-Hecke algebra is commutative while the "normal" hecke algebra is not (and I think the first is the center of the second by some Bernstein theorem?) | |
| Feb 14, 2018 at 11:10 | history | answered | Will Sawin | CC BY-SA 3.0 |