Vertex representations via finite groups and the McKay correspondence
Abstract
Given a finite group
Γ
and a virtual character $\wt$ on it, we construct a Fock space and associated vertex operators in terms of representation ring of wreath products
Γ∼
S
n
. We recover the character tables of wreath products
Γ∼
S
n
by vertex operator calculus. When
Γ
is a finite subgroup of
S
U
2
, our construction yields a group theoretic realization of the basic representations of the affine and toroidal Lie algebras of
ADE
type, which can be regarded as a new form of McKay correspondence.