Timeline for Tamagawa number of GL(n)
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 22, 2018 at 23:56 | comment | added | Jim Humphreys | General linear groups are certainly connected. How do you define this notion? | |
| Nov 20, 2018 at 22:31 | comment | added | Jim Humphreys | There is quite a range of literature by now on Tamagawa numbers, including Weil's informal lectures published more formally as a 1982 volume in the PM series Adeles and Algebraic Groups. See especially Chapter III in the long paper by J. Oesterle in Invent. Math. 76 (`984), which confirms that the Tamagawa number of a general linear group is 1 (over a relevant field). Note by the way that Kottwitz finished off the Tamagawa conjejcture by dealing with a tricky exceptional type. Most of the literature is aimed at such cases: simply connected semisimple groups over number fields. | |
| Nov 20, 2018 at 21:38 | comment | added | Not a grad student | I think the answer is just 1. Since $GL_n = SL_n \times \mathbb{G}_m$, $\tau(GL_n)=\tau(SL_n) \tau(\mathbb{G}_m)=1 \times 1 = 1$. | |
| Nov 20, 2018 at 11:04 | comment | added | user130903 | Have you looked at: Tamagawa number of reductive algebraic groups. Lai, K. F. Compositio Mathematica, Volume 41 (1980) no. 2, p. 153-188? | |
| Nov 20, 2018 at 5:58 | history | asked | Tian An | CC BY-SA 4.0 |