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