Timeline for Shimura correspondence for automorphic forms on other groups
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 5, 2019 at 10:01 | vote | accept | thislife | ||
| Sep 4, 2019 at 21:07 | comment | added | Marty | @GTA -- Savin describes an isomorphism between the Iwahori-Hecke algebra of a covering group (e.g. an d-fold cover of SL_n) and the Iwahori-Hecke algebra of a related linear group (e.g., a linear quotient of SL_n, determined by d and n). It turns out that this isomorphism reflects an isomorphism of L-groups (using my L-group for the covering group), so it's an instance of functoriality. Presumably some of these may arise from global correspondences between automorphic forms on a covering and a linear group. | |
| Sep 4, 2019 at 19:41 | comment | added | GTA | Maybe it's a trivial question, but how does Hecke algebra correspondence fit into functoriality? | |
| Sep 4, 2019 at 19:36 | comment | added | Marty | @GTA -- Well, sort of. First, one has to have an L-group for covering groups, so that functoriality makes sense. And then one can check that various correspondences are functorial. Examples include the metaplectic correspondence (e.g., recent work of Gan and Savin), and Hecke algebra correspondences. For theta correspondences, there are interesting cases to check functoriality -- e.g., $SL_3$ and a double cover of $SL_3$ (or quasisplit $SU_3$ and its double-cover), which form a dual pair in a double cover of $F_4$. Wee Teck Gan and I may finish that someday..... | |
| Sep 4, 2019 at 7:06 | comment | added | GTA | Does this somehow enable us to see some other theta correspondences as instances of Langlands functoriality? | |
| Sep 4, 2019 at 5:18 | history | answered | Marty | CC BY-SA 4.0 |