Timeline for Double coset spaces of reductive groups and integral representations of L-functions
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Oct 12, 2011 at 19:13 | vote | accept | B R | ||
| Mar 30, 2011 at 18:44 | comment | added | B R | Thanks! I see that Helminck has a lot of interesting papers on his website. Proposition 6.10 in the paper you mention seems to simplify the double-coset calculation to something more tractable: Let $A_i$ be representatives of the $H_k$-conjugacy classes of $\theta$-stable maximal $k$-split tori in $G$, then $$H_k\backslash G_k/P_k=\bigcup_{i\in I} W_{H_k}(A_i)\backslash W_{G_k}(A_i)$$ here $H$ is a $k$-open subgroup of the fixed points of the involution $\theta$ and $P$ is a minimal parabolic. | |
| Mar 30, 2011 at 14:59 | answer | added | Ramin | timeline score: 8 | |
| Mar 30, 2011 at 13:16 | comment | added | user1832 | You may find S.P.Wang and A.G.Helminck's paper 'on rationality properties of involutions of reductive groups' helpful, in which they showed that when $H_k$ is an open subgroup of the fixed point of an involution of $G_k$, then the double coset $P_k\G_k/H_k$ is finite when $k$ is a local field. When $k$ is global, they also gave an example with infinite double cosets. | |
| Mar 30, 2011 at 6:24 | history | asked | B R | CC BY-SA 2.5 |