Timeline for What is the algebraic fundamental groups of $SO(n)$ and $Sp(2n)$?
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| Oct 10, 2015 at 17:44 | comment | added | Mikhail Borovoi | You ask about $\pi_1(G)$, where $G=(\mathrm{SL}_n)^\sigma$ and $\sigma$ is an involution. Such $\sigma$ and $G$ are classified, see the book by Onishchik and Vinberg (1990), Table 7. They are $\mathrm{Sp}_{2m}$ for $2m=n$, $\mathrm{O}_n$ (not $\mathrm{SO}_n$), and $\mathrm{S}(\mathrm{GL}_p\times \mathrm{GL}_{n-p})$. For the last group we have $\pi_1(G)=\mathbb{Z}$. | |
| Oct 10, 2015 at 17:05 | comment | added | Gest2015 | oh that's a wonderful and complete answer, by the way I was reading you memoir this morning! thanks. | |
| Oct 10, 2015 at 17:03 | vote | accept | Gest2015 | ||
| Oct 10, 2015 at 14:08 | history | edited | Mikhail Borovoi | CC BY-SA 3.0 |
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| Oct 10, 2015 at 13:46 | history | edited | Mikhail Borovoi | CC BY-SA 3.0 |
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| Oct 10, 2015 at 13:41 | history | answered | Mikhail Borovoi | CC BY-SA 3.0 |