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Hello everyone

I would like to learn basic theory of the Chevalley Groups. There are several references for this subject, like "Introduction to Lie algebras and representation theory" by Humphreys, and Steinberg notes on the Chevalley groups.

Do you know any other references beside these two books?

Thank you

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  • $\begingroup$ For the classical groups you can also take a look at the very nice and accessible book "The Geometry of the Classical Groups" by Donald E. Taylor. $\endgroup$
    – j.p.
    Apr 25, 2012 at 15:20
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    $\begingroup$ "Chevalley groups" (and twisted analogues) have a special place in the general study of linear algebraic groups and are attractive to study on their own. The basic Lie algebra set-up, with Chevalley basis and beginning steps toward construction of the groups, can be found in my book or in a late chapter of the Bourbaki treatise on Lie groups and Lie algebras. But Carter's 1972 book, now scarce and/or unaffordable outside some libraries, is the only book treating the group structure in a patient style. Steinberg's notes (still online at UCLA) provide extra breadth. Good luck. $\endgroup$ Apr 26, 2012 at 23:27

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It doesn't contain any representation theory, but I think that Carter's book "Simple Groups of Lie Type" is an excellent place to start. Steinberg's notes have a lot more stuff in them, but Carter's book is an easier read.

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There is a new book: "Linear Algebraic Groups and Finite Groups of Lie Type" by Gunter Malle and Donna Testerman (Cambridge Univesity Press, 2011). The first part is an introduction to linear algebraic groups, and the third part is on finite groups of Lie type).

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There is a nice survey of Chevalley groups written by Elias Weber, which concerns the construction of the groups and the structure through its relevent subgroups. It also contains information regarding the representation theory. This would be a good place to read from once you understand the subject more. Link: http://sma.epfl.ch/~testerma/doc/projets/Weber_Chevalleygroups.pdf

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