There is a substantial amount of work that has been done on
the loose idea of series of Lie groups but which has not been
published. This page gives some links to unpublished work.
Pierre Vogel
This is Pierre Vogel's homepage with links to his unpublished papers.
Dylan Thurston
This is Dylan Thurston's preprint which reports on a computer
calculation which shows that the F4 series and the E6 series only
have finitely many points.
Predrag Cvitanovic
This is Predrag Cvitanovic's electronic book "Group Theory".
This is work in progress.
Predrag Cvitanovic This is the preprint
"Classical and exceptional Lie algebras as invariance algebras"
by Predrag Cvitanovic. This was published as preprint by the
Department of Theoretical Physics, University of Oxford but it
is now unavailable.
Tony Smith This is a page which (amongst other things)
gives all 5-step gradings (Type II) on simple Lie algebras.
Automorphic forms The formula (64) gives the spherical
vector for the simply laced exceptional groups parametrised
by s=m/2. The case s=1/2 m=1 corresponds to F_4. This is not
simply laced and is not included. The term I_3 is related
to cubic Jordan algebras.
The exceptional series was discovered independently in
integrable field theory.

MR1984741 (2005a:82028) Dorey, Patrick ; Pocklington, Andrew ; Tateo, Roberto . Integrable aspects of the scaling $q$-state Potts models. I. Bound states and bootstrap closure.
Nuclear Phys. B 661 (2003), no. 3, 425--463.
Another hint may be the Rogers or ultraspherical polynomials
as discussed in 1.4.1 for k=0,1/2,1,2. There is an obvious question
for k=4 we should get K\G/K for G=G_2 and we may get an interpretation
for k=3 in terms of the sextonions.

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