Quantum vertex representations via finite groups and the McKay correspondence
Abstract
We establish a
q
-analog of our recent work on vertex representations and the McKay correspondence. For each finite group
Γ
we construct a Fock space and associated vertex operators in terms of wreath products of
Γ×
C
×
and the symmetric groups.
An important special case is obtained when
Γ
is a finite subgroup of
S
U
2
, where our construction yields a group theoretic realization of the representations of the quantum affine and quantum toroidal algebras of
ADE
type.