Notational conventions
We adopt the following conventional notation:
C field of complex numbers
¥q finite field with q elements, q (^ 1) being a prime power
(thus, by a prime power we always mean a prime to
a positive integer power)
N set of nonnegative integers 0,1,2,...
Q field of rational numbers
R field of real numbers
Z ring of integers
Z
+
set of positive integers 1,2,...
A ground field or (commutative) ring over which algebras and representa-
tions are defined is usually written in Zapf Chancery fonts. In particular,
we use the following notation throughout the book:
^, ^C ground fields, with ^ often algebraically closed
^ a (commutative) ground ring
Z :— Z ^ ^
- 1
] , the ring of Laurent polynomials over Z in an
indeterminate v
Si := Z[/], where q
v2
We also make the following conventions:
A C B means A is a subset of B, while A C B means A is a proper
subset of B: and
xxiu
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