Equivariant K-theory, wreath products, and Heisenberg algebra
Abstract
Given a finite group G and a G-space X, we show that a direct sum $F_G (X) = \bigoplus_{n \geq 0}K_{G_n} (X^n) \bigotimes \C$ admits a natural graded Hopf algebra and
λ
-ring structure, where
G
n
denotes the wreath product
G∼
S
n
.
F
G
(X)
is shown to be isomorphic to a certain supersymmetric product in terms of $K_G(X)\bigotimes \C$ as a graded algebra. We further prove that
F
G
(X)
is isomorphic to the Fock space of an infinite dimensional Heisenberg (super)algebra. As one of several applications, we compute the orbifold Euler characteristic
e(
X
n
,
G
n
)
.