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In the his book

Linear algebraic groups, by T.A. Springer,

there is a list of possible Tits-Indexes. For the $E_7$ case, there is an index shown, such that vertex $1$ and $7$ are circled (Bourbaki notation). I just realized that yesterday by coincidence. However in Tits's original paper this index is not listed. On top of that neither here

http://arxiv.org/pdf/1511.02538.pdf

nor here

http://arxiv.org/abs/0807.2140

do we find it.

What did go wrong in Springers book?

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    $\begingroup$ There must be lots of disappointed people coming here from the Hot Network Questions list. *cough* $\endgroup$ Jun 30, 2016 at 16:35
  • $\begingroup$ I didnt intend to troll. Changed the title. $\endgroup$
    – nxir
    Jun 30, 2016 at 18:15

1 Answer 1

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That is a typo. In index 14 on p. 321 the vertex 6 should be black. In Proposition 17.8.2, this index is correct. It corresponds to $E_{7,3}^{28}$ in Tits' notation.

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  • $\begingroup$ This is a helpful correction to the second edition of Springer's book, but unfortunately there is usually no practical way to find current lists of such corrections. In the old days when books were typically typeset by hand and publishers made fixed press runs (which often created tax problems for unsold warehoused books), it was common to issue corrected reprints. But now authors supply LaTeX, from which expensive printing plates are made and on-demand copies are printed. So publishers are reluctant to do corrections. I make my own lists of minor misprints found in such books. $\endgroup$ Jun 30, 2016 at 19:36
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    $\begingroup$ This screams for setting up a online archive of typos and wrong results. I and my dissertation supervisor lost some time arguing about this wrong listed Tits-Index, for example. $\endgroup$
    – nxir
    Jul 1, 2016 at 13:00

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