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Oct 8, 2015 at 18:28 comment added Allen Knutson Among "standard textbooks" let me recommend Jim Humphreys' "Reflection groups and Coxeter groups".
Oct 8, 2015 at 15:43 comment added David Chow $E_{7(7)}$ refers to the split real form, not the complex $E_7$.
Oct 8, 2015 at 14:25 comment added Jim Humphreys The question is out of focus, starting with "the $E_7(7)$ Lie group". It's not clear what this means, but the invariant theory of the associated Weyl group does lead to a polynomial ring of invariants (Chevalley) geneerated by algebraically independent homogeneous polynomials of degrees $d$ which you've listed with the index $k$. This in turn provides a picture of invariants in the simple complex Lie algebra of type $E_7$ via Harish-Chandra's isomorphism. All of this is found in standard textbooks, so I think the question is not currently at research-level.
Oct 8, 2015 at 13:52 history edited Stefan Kohl CC BY-SA 3.0
Added LaTeX markup and top-level tag.
Oct 8, 2015 at 13:47 review First posts
Oct 8, 2015 at 13:52
Oct 8, 2015 at 13:39 history asked Geoffrey Compere CC BY-SA 3.0