  In 1983, Lusztig defined a map $\sigma$ from affine permutations of $n$ to
partitions of $n$. He conjectured that for any partition $\lambda$ of $n$,
$\sigma^{-1}(\lambda)$ is a two-sided cell. Shi, in 1986, proved part of this
conjecture. As a byproduct, he introduced the Shi arrangement of hyperplanes
and found a few of its remarkable properties. The Shi arrangement has since
become a central object in algebraic combinatorics. This article is intended to
be a fairly gentle introduction to the Shi arrangement, intended for readers
with a modest background in combinatorics, algebra, and Euclidean geometry.

Combinatorics