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