Notation
T
n
G
nG
Gc,
B
(Ga)o^a^a
Sreg? 0
re
g
TcG
t
tz
k
vc,
a - b
AnnV
n-dimensional torus
compact connected Lie group;
in Chap. 5 and Appendix A, a compact real-analytic manifold;
in Chap. 6, a compact connected semisimple Lie group;
order of the matrix group R n c X n G in which G is embedded (p. 10)
complexification of G (p. 10), local complexification of G (p. 27,32)
Lie algebra of G
set of regular points of adjoint (resp. co-adjoint) action (p. 8)
fixed maximal torus
Lie algebra of T;
in Chap. 5 and Appendix A, an arbitrary real vector space
period lattice of Assumption A (p. 28);
in Chap. 12, the integral lattice of T in t
dimension of t
complexification and annihilator of a space V
fixed Ad-invariant inner product on g, extended
to a C-bilinear form on g c (p. 9);
in Chap. 6, minus the Killing form (p. 31);
in Chap. 5 and Appendix A, an arbitrary inner product on t,
and its extension to t c (p. 27)
t1- = [g, t] orthogonal of t in g (pp. 8,9)
t, t1- annihilators of tr1, t (p. 9)
if isomorphism g g* induced by Ad-invariant
inner product on g (p. 9)
i restriction t —• t* of natural projection g* t* (p. 10)
to Weyl chamber (p. 8);
in Chap. 5 and Appendix A, a certain open subset of t (p. 27)
W Weyl chamber in g* (p. 9)
tj = i(W) Weyl chamber (p. 10)
LUQ, LUG symplectic structure on G x tj (resp. G x to) (pp. 10,11,54)
B ^ , B G one-form on G x tg (resp. G x to) with
(IQQ = CJQ (resp. dQc ^G) (pp. H54)
see p.11
see p.11
see p. 11
inverse of ad
p
: t±c - t±c (p. 11);
in Part 2, inverse of £ i-» ad^(i _ 1 (p)) : t-1 t x (p. 55)
see p.12
see pp. 12,56
(£0.,r0){g
toC
Xp
ZH,
dH
dg
&•*
TH
dH
' dp
,P)
d
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